Probability Theory and Stochastic Processes
The ultimate objective of this book is to present a panoramic view of the main stochastic processes which have an impact on applications, with complete proofs and exercises. Random processes play a central role in the applied sciences, including operations research, insurance, finance, biology, phys...
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| Format: | eBook |
| Language: | English |
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Cham
Springer International Publishing
2020, 2020
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| Edition: | 1st ed. 2020 |
| Series: | Universitext
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Introduction.-Warming Up
- Integration Theory for Probability
- Probability and Expectation
- Convergence of random sequences
- Markov Chains
- Martingale Sequences
- Ergodic Sequences
- Generalities on Stochastic Processes
- Poisson Processes
- Continuous-Time Markov Chains
- Renewal Theory in Continuous Time
- Brownian Motion
- Wide-sense Stationary Stochastic Processes
- An Introduction to Itô’s Calculus
- Appenndix: Number Theory and Linear Algebra
- Analysis
- Hilbert Spaces
- Z-Transforms
- Proof of Paul Lévy’s Criterion
- Direct Riemann Integrability
- Bibliography
- Index.