Essentials of Stochastic Processes 3rd Edition by Richard Durrett 331945613X 9783319456133

Essentials of Stochastic Processes 3rd Edition by Richard Durrett – Ebook PDF Instant Download/Delivery. 331945613X, 9783319456133

Full download Essentials of Stochastic Processes 3rd Edition after payment

Product details:

ISBN 10: 331945613X

ISBN 13: 9783319456133

Author: Richard Durrett

Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding.    Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatment of other topics useful for applications has been expanded.  In addition, the ordering of topics has been improved; for example, the difficult subject of martingales is delayed until its usefulness can be applied in the treatment of mathematical finance.

Essentials of Stochastic Processes 3rd Table of contents:

1 Markov Chains

1.1 Definitions and Examples

1.2 Multistep Transition Probabilities

1.3 Classification of States

1.4 Stationary Distributions

1.4.1 Doubly Stochastic Chains

1.5 Detailed Balance Condition

1.5.1 Reversibility

1.5.2 The Metropolis–Hastings Algorithm

1.5.3 Kolmogorow Cycle Condition

1.6 Limit Behavior

1.7 Returns to a Fixed State

1.8 Proof of the Convergence Theorem*

1.9 Exit Distributions

1.10 Exit Times

1.11 Infinite State Spaces*

1.12 Chapter Summary

Recurrence and Transience

Stationary Distributions

Convergence Theorems

Exit Distributions

Exit Times

1.13 Exercises

Understanding the Definitions

Two State Markov Chains

Chains with Three or More States

Exit Distributions and Times

More Theoretical Exercises

Infinite State Space

2 Poisson Processes

2.1 Exponential Distribution

2.2 Defining the Poisson Process

2.2.1 Constructing the Poisson Process

2.2.2 More Realistic Models

2.3 Compound Poisson Processes

2.4 Transformations

2.4.1 Thinning

2.4.2 Superposition

2.4.3 Conditioning

2.5 Chapter Summary

2.6 Exercises

Exponential Distribution

Poisson Approximation to Binomial

Poisson Processes: Basic Properties

Random Sums

Thinning and Conditioning

More Theoretical Exercises

3 Renewal Processes

3.1 Laws of Large Numbers

3.2 Applications to Queueing Theory

3.2.1 GI/G/1 Queue

3.2.2 Cost Equations

3.2.3 M/G/1 Queue

3.3 Age and Residual Life*

3.3.1 Discrete Case

3.3.2 General Case

3.4 Chapter Summary

3.5 Exercises

Age and Residual Life

4 Continuous Time Markov Chains

4.1 Definitions and Examples

4.2 Computing the Transition Probability

4.2.1 Branching Processes

4.3 Limiting Behavior

4.3.1 Detailed Balance Condition

4.4 Exit Distributions and Exit Times

4.4.1 Exit Distribution

4.4.2 Exit Times

4.5 Markovian Queues

4.5.1 Single Server Queues

4.5.2 Multiple Servers

4.5.3 Departure Processes

4.6 Queueing Networks*

4.7 Chapter Summary

4.8 Exercises

Hitting Times and Exit Distributions

Markovian Queues: Finite State Space

Markovian Queues: Infinite State Space

Queueing Networks

5 Martingales

5.1 Conditional Expectation

5.2 Examples

5.3 Gambling Strategies, Stopping Times

5.4 Applications

5.4.1 Exit Distributions

5.4.2 Exit Times

5.4.3 Extinction and Ruin Probabilities

5.4.4 Positive Recurrence of the GI/G/1 Queue*

5.5 Exercises

6 Mathematical Finance

6.1 Two Simple Examples

6.2 Binomial Model

6.2.1 One Period Case

6.2.2 N Period Model

6.3 Concrete Examples

6.4 American Options

6.5 Black–Scholes Formula

6.5.1 The Black–Scholes Partial Differential Equation

6.6 Calls and Puts

6.7 Exercises

A Review of Probability

A.1 Probabilities, Independence

A.1.1 Conditional Probability

A.2 Random Variables, Distributions

A.3 Expected Value, Moments

A.4 Integration to the Limit

People also search for Essentials of Stochastic Processes 3rd: 

essentials of stochastic processes pdf

essentials of stochastic processes solution pdf

essentials of stochastic processes solution manual pdf

 essentials of stochastic processes durrett