Probability Theory and Stochastic Processes with Applications (Oliver Knill)

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Probability Theory and Stochastic Processes with Applications (Oliver Knill)

In this book, discrete and continuous stochastic processes, as well as their applications, are introduced. Its distinctive methodology offers a thorough introduction to the interesting field of probability theory.

The textual summary of the book is provided in the introduction, along with a few well-known pop culture puzzles like renowned paradoxes; mathematics begins in chapter 2. In-depth coverage of measure theory and real analysis is provided. The central limit theorem and the law of the iterated log mark the chapter's conclusion. This is all fairly common information that is often addressed in a rigorous probability theory course. Martingales and discrete stochastic processes are discussed in Chapter 3. Brownian motion and stochastic differential equations are covered in Chapter 4 along with other continuous stochastic processes. Additionally, chapters 3 and 4 include information that is typically covered in a second graduate course and is quite conventional. Chapter 5 is special and makes the book unique.

Percolation, random matrices, estimation theory (Rao Cramer), Vlasov dynamics, multivariate distributions, Poisson processes, random maps, circular random variables (central limit theorem for those), lattice points close to Brownian paths, arithmetic random variables, symmetric diophantine equations, and random variables with singular continuous laws are just a few of the topics that have been chosen.

Ebook Details

About the Authors
Oliver Knill is a Preceptor in Mathematics, at Harvard University.
Published Date / Year
(August 12, 2009); eBook (2009)
The PDF is post by the author, the copyright holder.
510 pages
eBook Format
PDF (27 MB) and DJVU (8 MB)

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