Second Order PDE's in Finite & Infinite Dimensions
Edition: 1 edition
Publisher: Springer
Published: June 27, 2001
Language: eng
Format: Paperback
Number of pages: 330
ISBN-13: 9783540421368
Subjects: Differential Equations; Integral equations; Probability & statistics; Partial Differential Equations; Stochastic Processes; Mathematics; Medical / Nursing; Science/Mathematics; General; Probability & Statistics - General; Mathematics / Differential Equations; Mathematics-Differential Equations; Mathematics-Probability & Statistics - General; Medical / General; Stochastic partial differentia; Stochastic partial differential equations
Description: This book deals with the study of a class of stochastic differential systems having unbounded coefficients, both in finite and in infinite dimension. The attention is focused on the regularity properties of the solutions and on the smoothing effect of the corresponding transition semigroups in the space of bounded and uniformly continuous functions. The application is to the study of the associated Kolmogorov equations, the large time behaviour of the solutions and some stochastic optimal control problems. The techniques are from the theory of diffusion processes and from stochastic analysis, but also from the theory of partial differential equations with finitely and infinitely many variables.