Introduction to stochastic processes / Gregory F. Lawler.

Format:

Book

Author/Creator:

Lawler, Gregory F., 1955-

Contributor:

Hazel M. Hussong Fund.

Language:

English

Subjects (All):

Stochastic processes.

Physical Description:

xiii, 234 pages : illustrations ; 25 cm

Edition:

Second edition.

Place of Publication:

Boca Raton : Chapman & Hall/CRC, 2006.

Summary:

Focusing on mathematical ideas rather than proofs, Introduction to Stochastic Processes, Second Edition provides quick access to important foundations of probability theory applicable to problems in many fields. Approaching all problems and theorems without any measure theory, the book provides a concise and informal introduction to stochastic processes evolving with time.

This concise, informal introduction is designed to meet the needs of students and professionals not only in mathematics and statistics, but in the many fields in which the concepts presented are also important, including computer science, economics, business, biological sciences, psychology, and engineering. It acquaints readers with the possibilities of applying stochastic processes in their work.

Contents:

0.2 Linear Differential Equations 1

0.3 Linear Difference Equations 3

1 Finite Markov Chains 9

1.2 Large-Time Behavior and Invariant Probability 14

1.3 Classification of States 17

1.3.1 Reducibility 19

1.3.2 Periodicity 21

1.3.3 Irreducible, aperiodic chains 22

1.3.4 Reducible or periodic chains 22

1.4 Return Times 24

1.5 Transient States 26

2 Countable Markov Chains 43

2.2 Recurrence and Transience 45

2.3 Positive Recurrence and Null Recurrence 50

2.4 Branching Process 53

3 Continuous-Time Markov Chains 65

3.1 Poisson Process 65

3.2 Finite State Space 68

3.3 Birth-and-Death Processes 74

3.4 General Case 81

4 Optimal Stopping 87

4.1 Optimal Stopping of Markov Chains 87

4.2 Optimal Stopping with Cost 93

4.3 Optimal Stopping with Discounting 96

5 Martingales 101

5.1 Conditional Expectation 101

5.2 Definition and Examples 106

5.3 Optional Sampling Theorem 110

5.4 Uniform Integrability 114

5.5 Martingale Convergence Theorem 116

5.6 Maximal Inequalities 122

6 Renewal Processes 131

6.2 Renewal Equation 136

6.3 Discrete Renewal Processes 144

6.4 M/G/1 and G/M/1 Queues 148

7 Reversible Markov Chains 155

7.1 Reversible Processes 155

7.2 Convergence to Equilibrium 157

7.3 Markov Chain Algorithms 162

7.4 A Criterion for Recurrence 166

8 Brownian Motion 173

8.2 Markov Property 176

8.3 Zero Set of Brownian Motion 181

8.4 Brownian Motion in Several Dimensions 184

8.5 Recurrence and Transience 189

8.6 Fractal Nature of Brownian Motion 191

8.7 Scaling Rules 192

8.8 Brownian Motion with Drift 193

9 Stochastic Integration 199

9.1 Integration with Respect to Random Walk 199

9.2 Integration with Respect to Brownian Motion 200

9.3 Ito's Formula 205

9.4 Extensions of Ito's Formula 209

9.5 Continuous Martingales 216

9.6 Girsanov Transformation 218

9.7 Feynman-Kac Formula 221

9.8 Black-Scholes Formula 223

9.9 Simulation 228.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Hazel M. Hussong Fund.

ISBN:

158488651X

OCLC:

64084881

Publisher Number:

9781584886518