PDF4PRO ⚡AMP

Modern search engine that looking for books and documents around the web

Example: confidence

Chapter 1 Markov Chains - Yale University

Chapter 1 Markov ChainsA sequence of random variablesX0,X1,..with values in a countable setSisa Markov chain if at any timen, the future states (or values)Xn+1,Xn+2,..depend on the historyX0,..,Xnonly through the present are fundamental stochastic processes that have many diverse applica-tions. This is because a Markov chain represents any dynamical system whosestates satisfy the recursionXn=f(Xn 1,Yn),n 1, whereY1, and identically distributed ( ) andfis a deterministic func-tion. That is, the new stateXnis simply a function of the last state andan auxiliary random variable. Such system dynamics are typical of those forqueue lengths in call centers, stresses on materials, waiting times in produc-tion and service facilities, inventories in supply Chains , parallel-processingsoftware, water levels in dams, insurance funds, stock prices, Chapter begins by describing the basic structure of a Markov chainand how its single-step transition probabilities determine its evolution.

Gambler’s Ruin. Consider a Markov chain on S= ... In this case, the outcome of the game depends on the Gambler’s fortune. When the fortune is i, the Gambler either wins or loses $1 with respective probabilities p i or q i, or breaks even (the fortune does not change) with probability r i. Another interpretation is that the state of the ...

Fullscreen Download
Loading..

Tags:

  Gamblers, Ruin, Gambler s ruin

Information

Domain:

Source:

Link to this page:

Please notify us if you found a problem with this document:

Spam in document Broken preview Other abuse

Transcription of Chapter 1 Markov Chains - Yale University

Documents from same domain

1. Markov chains - Yale University

www.stat.yale.edu

Markov chains are a relatively simple but very interesting and useful class of random processes. A Markov chain describes a system whose state changes over time.

  Chain, Markov, Markov chain

Single-Stock Circuit Breakers - Yale University

www.stat.yale.edu

The single-stock circuit breakers will pause trading in any component stock of the Russell 1000 or S&P 500 Index in the event that the price of that stock has moved 10 percent or more in the preceding ve minutes. The pause generally will last ve minutes, and is intended to give the

  Breaker, Single, Circuit, Stocks, Single stock circuit breakers

Chapter 12 Multivariate normal distributions - Yale University

www.stat.yale.edu

Page 1 Chapter 12 Multivariate normal distributions The multivariate normal is the most useful, and most studied, of the standard joint dis-tributions in probability.

  Chapter, Normal, Probability, Multivariate, Multivariate normal

Chapter 3 Total variation distance between measures

www.stat.yale.edu

2 Chapter 3: Total variation distance between measures total variation distance has properties that will be familiar to students of the Neyman-Pearson approach to hypothesis testing. The Hellinger distance is closely related to the total variation distance—for example, both distances define

  Chapter, Total, Variations, Chapter 3, Chapter 3 total variation, Total variation

The bigmemory Package: Handling Large Data Sets in R …

www.stat.yale.edu

2 The bigmemory Package The new package bigmemory bridges the gap between R and C++, implementing massive matrices in memory and supporting their basic manipulation and exploration.

  Packages, Bigmemory package, Bigmemory

Seminar Notes: The Mathematics of Music - Yale University

www.stat.yale.edu

Understanding Musical Sound 1.1 Sound, the human ear, and the sinusoidal wave 1.1.1 Sound waves and musical notation Music is organized sound, and it is from this standpoint that we begin our study. In the world of Western music, notation has been developed to describe music in a very precise way. Consider, for instance, the following lines of ...

  Music, Musical, Of music, And musical

Chapter 7 Continuous Distributions - Yale University

www.stat.yale.edu

7. Continuous Distributions 5 Example <7.5> Zero probability for ties with continuous distributions. Calculations are also greatly simpli ed by the fact that we can ignore contributions from higher order terms when working with continuous distri-butions and small intervals. Example <7.6> The distribution of the order statistics from the uniform

  Chapter, Distribution, Continuous, Probability, Continuous distribution, Butions, Distri, Continuous distri butions

Chapter 12 Conditional densities

www.stat.yale.edu

Conditional densities 12.1Overview Density functions determine continuous distributions. If a continuous distri-bution is calculated conditionally on some information, then the density is called a conditional density. When the conditioning information involves another random variable with a continuous distribution, the conditional den-

  Chapter, Random, Conditional, Densities, Chapter 12 conditional densities

Chapter 9 Poisson processes - Yale University

www.stat.yale.edu

A Poisson process with rate‚on[0;1/is a random mechanism that gener- ates “points” strung out along [0 ; 1 / in such a way that (i) the number of points landing in any subinterval of lengtht is a random variable with

  Green

Chapter 10 Joint densities - Yale University

www.stat.yale.edu

and Y have continuous distributions, it becomes more important to have a systematic way to describe how one might calculate probabilities of the form Pf.X;Y/2Bgfor various sub- ... blobs, small shapes that don’t have any particular name—whatever suits the needs of a par-ticular calculation. <10.2> Example.

  Phases, Chapter, Distribution, Joint, Densities, Chapter 10 joint densities

Related documents

1 Gambler’s Ruin Problem - Columbia University

www.columbia.edu

1 Gambler’s Ruin Problem Consider a gambler who starts with an initial fortune of $1 and then on each successive gamble either wins $1 or loses $1 independent of the past with probabilities p and q = 1−p respectively. Let R n denote the total fortune after the nth gamble. The gambler’s objective is to reach a total

  University, Columbia university, Columbia, Gamblers, Ruin, Gambler s ruin

ONE-DIMENSIONAL RANDOM WALKS

galton.uchicago.edu

Gambler’s Ruin. Simple random walk describes (among other things) the fluctuations in a speculator’s wealth when he/she is fully invested in a risky asset whose value jumps by either 1 in each time period. Although this seems far too simple a model to be of any practical value,

  Dimensional, Walk, Random, Gamblers, Ruin, Gambler s ruin, One dimensional random walks

1 Stopping Times - Columbia University

www.columbia.edu

1. (First passage/hitting times/Gambler’s ruin problem:) Suppose that X has a discrete state space and let ibe a xed state. Let ˝= minfn 0 : X n= ig: This is called the rst passage time of the process into state i. Also called the hitting time of the process to state i. More generally we can let Abe a collection of states such

  University, Columbia university, Columbia, Gamblers, Ruin, Gambler s ruin

Chapter 6 - Random Processes - UAH

www.ece.uah.edu

random walk have been studied over the years (i.e., the gambler's ruin, drunken sailor, etc.). At first, a discrete random walk is introduced. Then, it is shown that a limiting form of the random walk is the well-known continuous Wiener process. Finally, simple equations are developed that

  Gamblers, Ruin, Gambler s ruin

Probability - University of Cambridge

www.statslab.cam.ac.uk

expectation. Random walks: gambler’s ruin, recurrence relations. Di erence equations and their solution. Mean time to absorption. Branching processes: generating functions and ex-tinction probability. Combinatorial applications of generating functions. [7] Continuous random variables: Distributions and density functions. Expectations; expec-

  Gamblers, Ruin, Gambler s ruin

Introduction to Stochastic Calculus - Duke University

services.math.duke.edu

i) The gambler’s ruin problem We play the following game: We start with 3$ in our pocket and we ip a coin. If the result is tail we loose one dollar, while if the result is positive we win one dollar. We stop when we have no money to bargain, or when we reach 9$. We may ask: what is the probability that I end up broke?

  Introduction, Calculus, Stochastic, Gamblers, Ruin, Gambler s ruin, Introduction to stochastic calculus

Essentials of Stochastic Processes - Duke University

services.math.duke.edu

To check this for the gambler’s ruin chain, we note that if you are still playing at time n, i.e., your fortune X n = i with 0 < i < N, then for any possible history of your wealth i n−1,i n−2,...i 1,i 0 P(X n+1 = i+1|X n = i,X n−1 = i n−1,...X 0 = i 0) = 0.4 since to increase your wealth by one unit you have to win your next bet. Here

  Gamblers, Ruin, Gambler s ruin

Random Walk: A Modern Introduction - University of Chicago

www.math.uchicago.edu

4.6 Green’s function for a set 96 5 One-dimensional walks 103 5.1 Gambler’s ruin estimate 103 5.1.1 General case 106 5.2 One-dimensional killed walks 112 5.3 Hitting a half-line 115 6 Potential Theory 119 6.1 Introduction 119 6.2 Dirichlet problem 121 6.3 Difference estimates and Harnack inequality 125 6.4 Further estimates 132

  Gamblers, Ruin, Gambler s ruin

Related search queries

Gambler’s ruin, Columbia University, Gambler, ONE-DIMENSIONAL RANDOM WALKS, Gambler's ruin, Introduction to Stochastic Calculus