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An Introduction to Probability and Stochastic Processes /
These notes were written as a result of my having taught a "nonmeasure theoretic" course in probability and stochastic processes a few times at the Weizmann Institute in Israel. I have tried to follow two principles. The first is to prove things "probabilistically" whenever possi...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York,
1993.
|
| Colección: | Springer texts in statistics,
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- I. Univariate Random Variables
- Discrete Random Variables
- Properties of Expectation
- Properties of Characteristic Functions
- Basic Distributions
- Absolutely Continuous Random Variables
- Basic Distributions
- Distribution Functions
- Computer Generation of Random Variables
- Exercises
- II. Multivariate Random Variables
- Joint Random Variables
- Conditional Expectation
- Orthogonal Projections
- Joint Normal Distribution
- Multi-Dimensional Distribution Functions
- Exercises
- III. Limit Laws
- Law of Large Numbers
- Weak Convergence
- Bochner's Theorem
- Extremes
- Extremal Distributions
- Large Deviations
- Exercises
- IV. Markov Chains--Passage Phenomena
- First Notions and Results
- Limiting Diffusions
- Branching Chains
- Queueing Chains
- Exercises
- V. Markov Chains--Stationary Distributions and Steady State
- Stationary Distributions
- Geometric Ergodicity
- Examples
- Exercises
- VI. Markov Jump Processes
- Pure Jump Processes
- Poisson Process
- Birth and Death Process
- Exercises
- VII. Ergodic Theory with an Application to Fractals
- Ergodic Theorems
- Subadditive Ergodic Theorem
- Products of Random Matrices
- Oseledec's Theorem
- Fractals
- Bibliographical Comments
- Exercises
- References
- Solutions (Sections I-V).