Stochastic Differential Equations and Applications (Dover Books on Mathematics)

This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications. The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and asymptotic estimates for solutions. The section concludes with a look at recurrent and transient solutions. Volume 2 begins with an overview of auxiliary results in partial differential equations, followed by chapters on nonattainability, stability and spiraling of solutions; the Dirichlet problem for degenerate elliptic equations; small random perturbations of dynamical systems; and fundamental solutions of degenerate parabolic equations. Final chapters examine stopping time problems and stochastic games and stochastic differential games. Problems appear at the end of each chapter, and a familiarity with elementary probability is the sole prerequisite.

Science & Math

Friedman, Prof. Avner

Mathematics

Dover Publications

This accessible and self-contained treatment provides even readers previously unacquainted with parabolic and elliptic equations with sufficient background to understand research literature. Author Avner Friedman — Director of the Mathematical Biosciences Institute at The Ohio State University — offers a systematic and thorough approach that begins with the main facts of the general theory of second order linear parabolic equations. Subsequent chapters explore asymptotic behavior of solutions, semi-linear equations and free boundary problems, and the extension of results concerning fundamental solutions and the Cauchy problem to systems of parabolic equations. The final chapter concerns questions of existence and uniqueness for the first boundary value problem and the differentiability of solutions, in terms of both elliptic and parabolic equations. The text concludes with an appendix on nonlinear equations and bibliographies of related works.

Partial Differential Equations of Parabolic Type (Dover Books on Mathematics)

This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists. Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of weak derivatives, proves various inequalities and imbedding problems, and derives smoothness theorems. Part Two concerns evolution equations in Banach space and develops the theory of semigroups. It solves the initial-boundary value problem for parabolic equations and covers backward uniqueness, asymptotic behavior, and lower bounds at infinity. The final section includes independent topics directly related to the methods and results of the previous material, including the analyticity of solutions of elliptic and parabolic equations, asymptotic behavior of solutions of elliptic equations near infinity, and problems in the theory of control in Banach space.

Partial Differential Equations (Dover Books on Mathematics)

This advanced graduate-level text examines variational methods in partial differential equations and illustrates their applications to a number of free-boundary problems. Detailed statements of the standard theory of elliptic and parabolic operators make this treatment readable for engineers, students, and nonspecialists alike. The text's first two chapters can be used for a single-semester graduate course in variational inequalities or partial differential equations. The succeeding chapters — covering jets and cavities, variational problems with potentials, and free-boundary problems not in variational form — are more specialized and self-contained. Readers who have mastered chapters 1 and 2 will be able to conduct research on the problems explored in subsequent chapters. Bibliographic remarks conclude each chapter, along with several problems and exercises.

Variational Principles and Free-Boundary Problems (Dover Books on Mathematics)

<div>This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications. The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and asymptotic estimates for solutions. The section concludes with a look at recurrent and transient solutions. Volume 2 begins with an overview of auxiliary results in partial differential equations, followed by chapters on nonattainability, stability and spiraling of solutions; the Dirichlet problem for degenerate elliptic equations; small random perturbations of dynamical systems; and fundamental solutions of degenerate parabolic equations. Final chapters examine stopping time problems and stochastic games and stochastic differential games. Problems appear at the end of each chapter, and a familiarity with elementary probability is the sole prerequisite.</div>

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

Books by Friedman, Prof. Avner

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

Stochastic Differential Equations and Applications (Dover Books on Mathematics)

Partial Differential Equations of Parabolic Type (Dover Books on Mathematics)

Partial Differential Equations (Dover Books on Mathematics)

Variational Principles and Free-Boundary Problems (Dover Books on Mathematics)

Stochastic Differential Equations and Applications (Dover Books on Mathematics)