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| Preface | p. 1 |
| Stochastic Processes. Definitions. Examples | p. 3 |
| The Kolmogorov consistency theorem. Classification of processes | p. 8 |
| Random Walks. Recurrence. Reneweal Theorem | p. 14 |
| Martingales. Inequalities for martingales | p. 21 |
| Theorems on the limit of a martingale | p. 27 |
| Stationary sequences. Ergodic theorem | p. 34 |
| Ergodic theorem. Metric transitivity | p. 39 |
| Regularization of a process. Continuity | p. 44 |
| Processes without discontinuities of the second kind | p. 50 |
| Continuity of processes with independent increments. Martingales with continuous time | p. 56 |
| Measurable processes | p. 61 |
| Stopping times. Associated [sigma]-algebras | p. 65 |
| Completely measurable processes | p. 69 |
| L[subscript 2]-theory | p. 73 |
| Stochastic integrals | p. 80 |
| Stationary processes. Spectral representations | p. 87 |
| Stationary sequences. Regularity and singularity | p. 93 |
| The prediction of a stationary sequence | p. 98 |
| Markov processes | p. 104 |
| Homogeneous Markov processes and associated semigroups | p. 110 |
| Homogeneous purely discontinuous processes. Conditions for their regularity | p. 115 |
| Processes with a denumerable set of states | p. 120 |
| Simple birth and death processes | p. 127 |
| Branching processes with particles of only one kind | p. 132 |
| Homogeneous processes and strongly continuous semigroups. Resolvent operator and generator | p. 137 |
| The Hille-Iosida theorem | p. 143 |
| Processes with independent increments. Representation of the discontinuous part | p. 149 |
| General representation of a stochastically continuous process with independent increments | p. 155 |
| Diffusion processes | p. 160 |
| Stochastic integrals | p. 166 |
| Existence, uniqueness, and properties of solutions of stochastic differential equations | p. 172 |
| Ito's formula with some corollaries | p. 178 |
| References | p. 184 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
Lectures on the Theory of Stochastic Processes
by Skorokhod, A. V.Format: Paperback
Pub. Date: 1996-12-01
Publisher(s): De Gruyter
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