Introduction to Random Processes
Today, the theory of random processes represents a large field of mathematics with many different branches, and the task of choosing topics for a brief introduction to this theory is far from being simple. This introduction to the theory of random processes uses mathematical models that are simple,...
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1987, 1987
|
| Edition: | 1st ed. 1987 |
| Series: | Springer Series in Soviet Mathematics
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- Section 1. Random Processes with Discrete State Space. Examples
- Section 2. Homogeneous Markov Processes with a Countable Number of States. Kolmogorov’s Differential Equations
- Section 3. Homogeneous Markov Processes with a Countable Number of States. Convergence to a Stationary Distribution
- Section 4. Branching Processes. Method of Generating Functions
- Section 5. Brownian Motion. The Diffusion Equation and Some Properties of the Trajectories
- Section 6. Random Processes in Multi-Server Systems
- Section 7. Random Processes as Functions in Hilbert Space
- Section 8. Stochastic Measures and Integrals
- Section 9. The Stochastic Ito Integral and Stochastic Differentials
- Section 10. Stochastic Differential Equations
- Section 11. Diffusion Processes. Kolomogorov’s Differential Equations
- Section 12. Linear Stochastic Differential Equations and Linear Random Processes
- Section 13. Stationary Processes. Spectral Analysis and Linear Transformations
- Section 14. Some Problems of Optimal Estimation
- Section 15. A Filtration Problem. Kalman-Bucy Filter
- Appendix. Basic Concepts of Probability Theory