This is a brief introduction to stochastic processes studying certain elementary continuous-time processes. After a description of the Poisson process and related processes with independent increments as well as a brief look at Markov processes with a finite number of jumps, the author proceeds to introduce Brownian motion and to develop stochastic integrals and ItÃ´'s theory in the context of one-dimensional diffusion processes. The book ends with a brief survey of the general theory of Markov processes. The book is based on courses given by the author at the Courant Institute and can be used as a sequel to the author's successful book Probability Theory in this series. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Stochastic Processes (Courant Lecture Notes)

Science & Math

S.R.S. Varadhan

Mathematics

American Mathematical Society

The theory of large deviations deals with rates at which probabilities of certain events decay as a natural parameter in the problem varies. This book, which is based on a graduate course on large deviations at the Courant Institute, focuses on three concrete sets of examples: (i) diffusions with small noise and the exit problem, (ii) large time behavior of Markov processes and their connection to the Feynman-Kac formula and the related large deviation behavior of the number of distinct sites visited by a random walk, and (iii) interacting particle systems, their scaling limits, and large deviations from their expected limits. For the most part the examples are worked out in detail, and in the process the subject of large deviations is developed. The book will give the reader a flavor of how large deviation theory can help in problems that are not posed directly in terms of large deviations. The reader is assumed to have some familiarity with probability, Markov processes, and interacting particle systems. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Large Deviations (Courant Lecture Notes) (Courant Lecture Notes in Mathematics)

Harmonic Analysis is an important tool that plays a vital role in many areas of mathematics as well as applications. It studies functions by decomposing them into components that are special functions. A prime example is decomposing a periodic function into a linear combination of sines and cosines. The subject is vast, and this book covers only the selection of topics that was dealt with in the course given at the Courant Institute in 2000 and 2019. These include standard topics like Fourier series and Fourier transforms of functions, as well as issues of convergence of Abel, Feier, and Poisson sums. At a slightly more advanced level the book studies convolutions with singular integrals, fractional derivatives, Sobolev spaces, embedding theorems, Hardy spaces, and BMO. Applications to elliptic partial differential equations and prediction theory are explored. Some space is devoted to harmonic analysis on compact non-Abelian groups and their representations, including some details about two groups: the permutation group and SO(3). The text contains exercises at the end of most chapters and is suitable for advanced undergraduate students as well as first- or second-year graduate students specializing in the areas of analysis, PDE, probability or applied mathematics.

Harmonic Analysis (Courant Lecture Notes, 31)

American Mathematical Society, Courant Institute of Mathematical Sciences at New York University

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Books by S.R.S. Varadhan

See the best price to sell, buy, or rent books by S.R.S. Varadhan. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Stochastic Processes (Courant Lecture Notes)

Large Deviations (Courant Lecture Notes) (Courant Lecture Notes in Mathematics)

Harmonic Analysis (Courant Lecture Notes, 31)