Stochastic differential equations and applications
Friedman, Avner
Stochastic differential equations and applications - Mineola: Dover Publications 1976. - xvi, 531 p.; pb. 22 cm. - 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.
9780486453590
Mathematics
Probabilities
Applied Mathematics
Stochastic Processes
Markov Processes
Brownian Motion
Stochastic Integral
Differential Equations
Martin-Girsanov Theorem
Kolmogorov equation
Transient solutions
Nonattalnability
Elliptic equations
519.2 / FRI
Stochastic differential equations and applications - Mineola: Dover Publications 1976. - xvi, 531 p.; pb. 22 cm. - 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.
9780486453590
Mathematics
Probabilities
Applied Mathematics
Stochastic Processes
Markov Processes
Brownian Motion
Stochastic Integral
Differential Equations
Martin-Girsanov Theorem
Kolmogorov equation
Transient solutions
Nonattalnability
Elliptic equations
519.2 / FRI
