Foundations of modern probability
著者
書誌事項
Foundations of modern probability
（Probability and its applications）
Springer, 1997
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
A study of the foundations of modern probability, covering topics such as stochastic integrals and quadratic variation, martingales and optional times, Feller processes and semigroups, and Poisson and pure jump type Markov processes.
目次
- Elements of measure theory
- processes, distributions, and independence
- random sequences, series, and sums
- characteristic functions and classical limit theorems
- conditioning and disintegration
- Martingales and optional times
- Markov property and discrete time chains
- random walk and renewal theory
- stationarity and ergodic theory
- Poisson and pure jump type Markov processes
- Gaussian processes and Brownian motion
- Skorohod embedding and invariance principles
- independent increment processes and null-arrays
- convergence of random processes, measures, and sets
- stochastic integrals and quadratic variation
- continuous martingales and Brownian motion
- Feller processes and semigroups
- SDEs and martingale problems
- local time, excursions, and additive functionals
- one-dimensional SDEs and diffusions
- connections with PDEs and potential theory
- predictability, compensation, and excessive functions
- semimartingales and stochastic integration.
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