Transient Notes

In: Science

Submitted By Mudumo
Words 3438
Pages 14
9. Recurrent and Transient States
9.1 Definitions
(n)
9.2 Relations between fi and pii
9.3 Limiting Theorems for Generating Functions
9.4 Applications to Markov Chains
(n)
9.5 Relations Between fij and pij
9.6 Periodic Processes
9.7 Closed Sets
9.8 Decomposition Theorem
9.9 Remarks on Finite Chains
9.10 Perron-Frobenius Theorem
9.11 Determining Recurrence and Transience when Number of
States is Infinite
9.12 Revisiting Statistical Equilibrium
9.13 Appendix. Limit Theorems for Generating Functions
304

9.1 Definitions
Define

(n)

fii = P {Xn = i, X1 = i, . . . , Xn−1 = i|X0 = i}

= Probability of first recurrence to i is at the nth step.

(n)

fi = fii =

fii = Prob. of recurrence to i. n=1 Def. A state i is recurrent if fi = 1.
Def. A state i is transient if fi < 1.
Define Ti = Time for first visit to i given X0 = 1. This is the same as
Time to first visit to i given Xk = i. (Time homogeneous)


mi = E(Ti |X0 = i) =

(n)

nfii = mean time for recurrence n=1 (n)

Note: fii = P {Ti = n|X0 = i}
305

Similarly we can define
(n)

fij = P {Xn = j, X1 = j, . . . , Xn−1 = j|X0 = i}
= Prob. of reaching state j for first time in n steps starting from X0 = i. fij =

∞ n=1 (n)

fij = Prob. of ever reaching j starting from i.

Consider fii = fi = prob. of ever returning to i.
If fi < 1, 1 − fi = prob. of never returning to i.
i.e.
1 − fi = P {Ti = ∞|X0 = i} fi = P {Ti < ∞|X0 = i}

306

TH. If N is no. of visits to i|X0 = i ⇒ E(N |X0 = i) = 1/(1 − fi )
Proof:

E(N |X0 = i) = E[N |Ti = ∞, X0 = i]P {Ti = ∞|X0 = i}
+E[N |Ti < ∞, X0 = i]P {Ti < ∞|X0 = i}

E(N |Xo = i) = 1 · (1 − fi ) + fi [1 + E(N |X0 = i)]

If Ti = ∞ ⇒ except for n = 0 (X0 = i) , there will never be a visit to ii.e. E(N |Ti = ∞, X0 = i) = 1. If Ti < ∞, there is sure to be one visit, say at Xk (Xk = i). But then
E(N |Ti < ∞, Xk = i) = E(N |Ti < ∞, X0 = i) by Markov property;
i.e.
E[N |Ti < ∞, X0 = i] = 1 + E[N |X0 = i]…...

Similar Documents

Notes

...between people in our rapidly advancing generation. In Paul Dooley and Winnie Holzman’s play Post-Its (Notes on a Marriage), we watch as two young people who are in love and newly married, begin to leave each other post its notes when they have no time for communication with one another. The author successfully tells an amazing love story using a unique means of communication. According to Anne Maydan Nicotera, “communication is critical to inter-personal relationships” (Nicotera). The notes vary from topics such as one not wanting to wake the other as they leave early for work, for tasks that need to be completed throughout the day. The audience, through the reading of the post- its notes views the couple’s life as it goes through the early stages of a relationship, to having a child, to a downhill slide of their relationship, the steady reconstruction of a marriage, and eventually it goes on until one of the two passes on. By leaving these post-its notes, the unnamed couple manages to have a basis of communication upon which they both are able to agree upon. They manage to find a convenient and effective way to convey what they need to say to one another through post-its notes, and even though things get rough, and arguments ensue, they find their strength and return to one another. Their relationship is refound with a clean slate, and although there are occasional spats in the notes, the audience can see that their relationship is much easier once they settled their......

Words: 1316 - Pages: 6

Transient Advantage Innovated

...close up and how the light interacts with it." View more of the artist's work at pacegaUery.com. S R T G IS STUCK. For too long the business world an inflection point. Thefieldof strategy needs to acT AE Y has been obsessed with the notion of building a sus- knowledge what a multitude of practitioners already tainable competitive advantage. That idea is at the know: Sustainable competitive advantage is now the core of most strategy textbooks; it forms the basis exception, not the rule. Transient advantage is the of Warren Buffett's investment strategy; it's central new normal. to the success of companies on the "most admired" lists. I'm not arguing that it's a bad idea—obviously, The Anatomy of a Transient Advantage it's marvelous to compete in a way that others can't Any competitive advantage—whether it lasts two imitate. And even today there are companies that seasons or two decades—goes through the same create a strong position and defend it for extended life cycle. (See "The Wave of Transient Advantage.") periods of time—firms such as GE, IKEA, Unilever, But when advantages arefleeting,firmsmust rotate Julius Berger, and Swiss Re. But it's now rare for a through the cycle much more quickly and more often, company to maintain a truly lasting advantage. Com- so they need a deeper understanding of the early and petitors and customers have become too unpredict- late stages than they would if they were able to mainable, and industries too amorphous. The forces at tain one......

Words: 3854 - Pages: 16

Note

...next semester; I think you didn’t know how to sing when the note is really high. And the teacher will help you about this, and your chin always up when you sing but you never realized that.” So at the very beginning of this semester I changed a class to this class, and want to improve my singing skill. And just like my mother said that I can’t put my chin down when I was singing. And professor also pointed out this problem. And my facial expression was not very rich when I was singing, that seems like that I didn’t put myself in to that song. Just like a mission to complete. I worked on the chin problem and also the sight singing. Fortunately, the experience of playing the piano made me identify the tone accurate. And I don’t have to spend much time on working this. Therefore, I work hard on controlling my chin, and I still can’t adapt it at the very beginning. But through my hard working I can really handle it now. And as for sight singing, during this semester, I often singing before a mirror and practice my facial expression. And it was working. Now I think my facial expression is much better than before. And there is another point, when there was a really high note that I can’t reach it by my voice before. However, during this semester, I learned how to use my throat to reach that high note. Although I can’t describe how to do this in English, I really felt that was really changed. I can reach some really high note now. Time passed really fast, and this semester will......

Words: 540 - Pages: 3

Notes

...Credit Cards ◾ Allows debtors(customers) to receive goods and services from suppliers (creditor) using credit cards and pay for them later. ◾ Types and Examples: • Bank- Mastercard and Visa • Travel and Entertainment- American Express • Oil Company- BP Oil • Retail store- Belk ◦ Installment sales credit ◾ A contract issued by the seller that requires intermittent payments at specified times such as bi-weekly or monthly ◾ Example • Rooms To Go Furniture Store ◦ consumer loans ◾ Requires debtors to make monthly payments of a specified amount for a period of time ◾ Example: • Borrowing $1,000 from a bank and agreeing to make $100 payments for 10 months • What is a promissory note? ◦ Promissory note- A written promise to repay based on a debtor’s excellent credit history. • Why is collateral or a cosigner used? ◦ The lender may need some guarantee that you will repay or to know that someone will be responsible for the loan....

Words: 275 - Pages: 2

Notes for Notes

...Pro, Setup Assistant starts. Setup Assistant helps you specify your Wi-Fi network, set up a user account, and transfer information from another Mac or PC. You can also transfer information from a Time Machine backup or other disk. If you’re migrating from another Mac, you might have to update software if the other Mac doesn’t have Mac OS X version 10.5.3 or later installed. To migrate from a PC, download the Migration Assistant from www.apple.com/migrate-to-mac, and install it on the PC you want to migrate from. After you start Setup Assistant on your MacBook Pro, you can leave it midprocess without quitting, move to the other computer if you need to update its software, and then return to your MacBook Pro to complete the setup. Note:  If you don’t use Setup Assistant to transfer information when you first start up your MacBook Pro, you can do it later using Migration Assistant. Open Migration Assistant in the Utilities folder in Launchpad. For help using Migration Assistant, open Help Center and search for “Migration Assistant.” Chapter 1 Ready, Set Up, Go 13 To set up your MacBook Pro: 1 In Setup Assistant, follow the onscreen instructions until you get to the “Transfer Information to This Mac” screen. 2 Do a basic setup, a setup with migration, or transfer information from a Time Machine backup or other disk: Â To do a basic......

Words: 13874 - Pages: 56

Note

...Notes : In the poem, as well as the movie, the two major female characters are Wealthow and Grendel's mother. Unlike the movie, neither of these characters have large roles in the poem. Both play their part but are described very little. Wealthow is often only called the "gold-ringed queen" and only exists to play "a noble woman who knew what was right" (Raffel, 31). Despite her noble status, Wealthow holds her tongue and is only mentioned when she serves Beowulf and his soldiers mead from a jeweled cup. Grendel's mother, on the other hand, plays a slightly bigger role, but only as an evil idenity. Her name is never revealed and she is only known as Grendel's mother, signifying that the male defines the female. Additionally, Grendel's mother is the only female character that poses a threat to Beowulf and his men. Unfortunately, she is portrayed as a "mighty water witch", insinuating that any woman who defied an man was evil and wicked (Raffel, 41). These two female characters demonstrate the Anglo-Saxon ideas that women should be figures rather than hold any real power. Notes how women have become stronger forces in the world, yet are still held back by men. In the movie, Grendel's mother is shown to be little more than a sex object in the eyes of men, which actual allows her to hold power over them. She is able to seduce Hrothgar and Beowulf, creating sons for her evil to live on through. These monsters eventually attack the men as the repercussions of the "sins of the......

Words: 1298 - Pages: 6

Reality Is Transient

...Influence is unavoidable; our reality is not of our own making Like a game, reality is dependent on a set of mutual laws and expectations rule-makers agree upon and there are penalties for those who go against the expectations of the majority such as the loss of a “life” or “game over”. Some have a lot invested in the game- wealth, time, effort, goals. Others see it for what it is; a projection of our imagination with a subjective sense of meaning. This game of life is far more complex than any board game like Chess or Monopoly because it represents a reality that offers greater levels of intricacy than which merely mimics or replicates an aspect or semblance of life itself. Reality is transient. Reality is determined through the consensus of the majority and therefore is subject to change when the consensus changes, as happened over five hundred years ago when people began to realise that the then dominant view of the universe as geocentric as flawed. However, such change in the paradigm is inevitably accompanied by conflict as society divides between those who wish to protect the status quo, such as the Catholic Church which attempted to suppress the discoveries of scientists like Galileo, whilst others, like Shakespeare, welcomed new thoughts as shown in the naming of his theatre as ‘The Globe’ built in 1599. Shakespeare was a humanist who explored the exciting new possibilities presented by the rise of science in his society, and in his play As You Like It,......

Words: 882 - Pages: 4

Notes

...Chapter 2 Notes: 2.1: Concept: programs must be carefully designed before they are written. During the design process, programmers use tools such as pseudo code and flowcharts to create models of programs. Key terms: Logic Error: A mistake that does not prevent the programming from running, but it causes incorrect results. Debugging: finding and correcting the code that caused the error. Program Development Cycle: the process of creating, debugging, and possibly changing the original program. The steps are as follows: Design the program write the code correct syntax errors test the executable code Debug the code Repeat necessary Customer: The person, group or organization that is asking you to write a program Software Requirement: A single function that the program must perform in order to satisfy the customer Algorithm: A set of well-defined logical steps that must be taken to perform a task. It must be translated into code before it can be given to the computer. Pseudo code: “Fake Code” used to model programs Flow charts: Diagrams that that graphically depicts the steps the steps that take place in a program. There are three types of symbols in a flow chart: 1. Ovals (Appear at the top and bottom of a flow chart, and are also referred to as terminal symbols. The start terminal symbol marks the program’s starting point and the end terminal symbols marks the program’s ending point) 2. Parallelogram (Used for both input and output......

Words: 384 - Pages: 2

Notes

...Criminal Law Exam Notes Contents EXTENDING CRIMINAL LIABILTY PARTICIPATION & ATTEMPT 11 Complicity 11 Accessory after the act (s347) 12 Joint Criminal Enterprise (acting in concert) 12 Doctrine of Innocent Agency 13 Accessories Before the Fact & Principals of the Second Degree 14 Actus Reus 14 Mens Rea 16 Doctrine of Common Purpose 16 ATTEMPT 20 Mens Rea (Heavily dependent on MR). 21 Actus Reus 21 LARCENY 24 Actus Reus 24 a. Taking & Carrying Away 24 b. Property Capable of Being Stolen 24 c. Property in Someone Else’s Possession 25 Abandoned by owner 26 d. Without Consent of the Person in Possession 26 Mens Rea 28 1. Intent to Deprive Permanently 28 2. Without a Claim of Right Made in Good Faith (bona fide) 30 3. Fraudulently 31 Temporal Coincidence 33 Larceny by Finding 33 Larceny by Trick 34 Larceny as a Bailee 38 ASSAULT 41 Degree of Injury 41 Common Assault 42 a. Psychic Assault 42 b. Battery 44 Mens Rea 47 Intentional Assault 47 Reckless Assault 47 Negligence 48 Aggravated Assault 48 a. Assault Occasioning Actual Bodily Harm (ABH) (section 59) 49 b. Reckless GBH or Wounding (section 35) 50 c. Maliciously Wounding/GBH with Intention to Inflict GBH (section 33) 51 SEXUAL ASSAULT 54 Actus Reus 54 a. Sexual Intercourse 54 b. Absence of Consent 55 Common law Rules 57 o Doctrine of marital immunity abolished at common law (L 1991) and under statute (s61T(a)......

Words: 31227 - Pages: 125

Notes

...accounting issues, where relevant. You should also evaluate the financial condition and performance of each company. You may wish to include projected financial statements and a valuation based on those projections. However, finance covers valuation in far more detail in finance, so valuation is not the crucial part of this write-up. Each group will have about 45 minutes for their presentation, depending on the number of groups. That will include five minutes for setup, twenty minutes for a presentation, and five minutes for questions. 4. Final Exam. The exam will consist of five or six questions taken from footnotes, financial statements, or articles. The exam may include any topic covered in this course. The exam is open-book, open-notes, and you may use computers, calculators, and the Internet (not including e-mail). Grading: Grading is based on a mid-term and final examination, a group case presentation, a group project, and class participation. Class participation grading begins Monday, 14 August; class participation in the accounting camp does not count toward your final grade. Grade weighting is as follows: Group project. Write-up and presentation 40% Final examination 35% Class participation 25% I assign numerical grades for each assignment (maximum of 100 points for each assignment). At the end of the term I weight scores by the above percentages, add scores for the four assignments, and rank scores from high to low. I......

Words: 2809 - Pages: 12

Notes

...08/26/2005 Notes for Aides Meeting How is the point system working for Kinder? For all other grade levels? Who is in the lead (I’d like to periodically announce this on morning announcements)? The Points are going great!! We came up with every week (Thursdays) letting you know who is in the lead! How are the sheets of paper going? The sheet are a keeper! We think that is great way to keep up with points. That way I can tally them right. How is the tracking chart/poster coming along? We decided not to laminate the poster board, and just decorate with all sort of treats so the kids will see it in the café. We came up with if the visual see what they will “Win” they will try harder. And the tracking I will keep up with and by you (Mrs. Reipe) announcing it they will know who is in the lead. Is there anything not working? Well its better now, the long Breakfast and lunch lines. They are running smoother now, guess it was just the first couple of weeks of school!!! How can we turn things up a notch and make things even better? (Movie on Fridays, if earned???) We thought that was a great Idea, it will keep a lot of kids at their seats and ready to sit down and eat and watch the movie!! Breakfast: What can be used to number the tables instead of taping the number? I know you came up with the little cones!!! Sounds Great! And Ms. A said she has a Cricut to make the Velcro numbers!! Is there anything that needs to be improved for breakfast? Make a definite cut,......

Words: 569 - Pages: 3

The Note

...The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note. The note....

Words: 271 - Pages: 2

The Transient Sublime and Mortality in “Ode to a Nightingale”

...何梓涵 12010007 To Professor Hou Yiling English Literature The Transient Sublime and Mortality in “Ode to a Nightingale” Composed during the most creative period in Keats’s brief poetic career, “Ode to a Nightingale” has long been regarded as one of the most refined works of his poetry. Previous criticism has comprehensively explored its themes of nature, beauty and mortality, as well as its demonstration of Keats’s notion of Negative Capability. But based on my research, few critical reviews have touched upon the point which I find clearly suggest itself in this poem: that the poet’s experience here depicted is not merely an escape into the realm of ideal beauty, but also an intoxication with the Romantic sublime. Between the sublime and his anticipated death, Keats builds an analogical connection from which he gains insights into both. Hence it is my endeavour in this paper to illustrate that in “Ode to a Nightingale”, Keats describes the entire process of his journey into and back from the sublime, after which he has to face again the transience of the sublime and the mortality of human life. Traditionally, most critics agree on the poem’s theme being the conflict between reality and the Romantic ideal of uniting with nature, among many other contrasts that are present throughout the poem. The most representative interpretation comes from Richard Fogle, who defines the principal stress of the poem as a struggle between ideal and actual, containing more particular antitheses...

Words: 2490 - Pages: 10

Notes

...us immediately id he/she fails to receive any reply from us for whatever reasons. Once confirmed, NO CANCELLATION request will be entertained. c) NO CANCELLATION &AMENDMENT allowed. d) Genting Rewards Card members are not entitled to earn rewards Point (RP) for Best Deal package. We wish to inform that the type of room assigned to you is automatically allocated by our system according to the room category you have booked. As such you may get an old or a newly renovated room. Should you have special requests or change of room types, a RM15 surcharge is applicable for each request. A surcharge of RM20 will be imposed for check-in at the front office counter for customers who are eligible for self check-in at the E-Kiosk. On another note, we would like to inform that effective 1st June 2015, a surcharge of RM20 per luggage will be charged for luggage delivery/collection services by the bell counter personnel. RM20 refundable deposit for each trolley is available for self luggage service. Transferability a) The room booking is non-transferable. b) Booking name must be the same person who will be check in. c) The person who made the credit card booking must be the same person who will be checking in. No payment can be made on behalf of another person. Check-in Standard of check-in time 3.00pm (All hotels) Standard or check-out time 12.00pm (All hotels except for First World Hotel) Standard of check-out time 11.00am (First World Hotel only) a) You need to......

Words: 664 - Pages: 3

Notes

...attempt to dictate my response. In these kinds of situations, children very clearly understand that history matters. * When you go into a doctor’s office for the first time, you invariably have to fill out an information sheet that asks about your medical history. Some of these forms are very detailed, asking questions that require information from rarely accessed memory banks. Why does a doctor ask these questions? The doctor is trying to construct an accurate picture of your state of health. Your health is heavily influenced by the past. Your heredity, past behaviors, past experiences are all important determinants and clues to your present condition. Whenever you return to the doctor, he or she pulls out a file which contains all the notes from past visits. This file is a history of your health. Doctors understand very clearly that the past matters. * Some of you might be thinking that these examples are not very compelling because they both deal with the very recent past—they are not what we think of when we think of history. Let me give one final example that is more to the point. In 1917 the Communists took control of Russia. They began to exercise control over how the history of their country ought to be told. They depicted the tsar as oppressive and cruel. The leaders of the revolution, on the other hand, were portrayed in a very positive light. The Communist government insisted that these leaders, and in particular Lenin, understood more clearly than any one......

Words: 13668 - Pages: 55