Advanced Stochastic Processes
by Jan A. Van Casteren
Publisher: Bookboon 2013
Number of pages: 404
In this book, which is basically self-contained, the following topics are treated thoroughly: Brownian motion as a Gaussian process, Brownian motion as a Markov process, Brownian motion as a martingale, Markov chains, renewal theory, the martingale problem, Ito calculus, cylindrical measures, ergodic theory, etc.
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by Oliver Knill - Overseas Press
This text covers material of a basic probability course, discrete stochastic processes including Martingale theory, continuous time stochastic processes like Brownian motion and stochastic differential equations, estimation theory, and more.
by S. Watanabe - Tata Institute of Fundamental Research
The author's main purpose in these lectures was to study solutions of stochastic differential equations as Wiener functionals and apply to them some infinite dimensional functional analysis. This idea was due to P. Malliavin.
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The aim is to introduce the basic problems of non-linear PDEs with stochastic and irregular terms. We explain how it is possible to handle them using two main techniques: the notion of energy solutions and that of paracontrolled distributions.
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An informal introduction to Stochastic Calculus, and especially to the Ito integral and some of its applications. The text concentrates on the parts of the course which the author found hard, there is little or no comment on more standard matters.