Stochastic Partial Differential Equations

Sergey Lototsky earned a Master’s degree in Physics in 1992 from the Moscow Institute of Physics and Technology, followed by a PhD in Applied Mathematics in 1996 from the University of Southern California. After a year-long post-doc at the Institute for Mathematics and its Applications and a three-year term as a Moore Instructor at MIT, he returned to the department of Mathematics at USC as a faculty member in 2000. He specializes in stochastic analysis, with emphasis on stochastic differential equations. He has supervised more than 10 PhD students and has held visiting positions at the Mittag-Leffler Institute in Sweden and at several universities in Israel and Italy.Boris Rozovsky earned a Master’s degree in Probability and Statistics, followed by a Ph.D. in Physical and Mathematical Sciences, both from the Moscow State (Lomonosov) University. He was Professor of Mathematics and Director of the Center for Applied Mathematical Sciences at the University of Southern California.  Currently, he is the Ford Foundation Professor of Applied Mathematics at Brown University.

“The objective of this textbook is to discuss as much of the SPDE-related material as possible without going too much into the details, and to prepare the reader for independent research in this area. … book contains a lot of exercises that are called problems, with subsequent discussion. The presentation is self-contained. In general, the book is beautifully presented and can be recommended for anybody who starts and continues with SPDEs, especially for undergraduate and postgraduate students, researchers and practitioners.” (Yuliya S. Mishura, zbMATH 1375.60010, 2018)

• Introduction.- Basic Ideas.- Stochastic Analysis in Infinite Dimensions.- Linear Equations: Square-Integrable Solutions.- The Polynomial Chaos Method.- Parameter Estimation for Diagonal SPDEs.- Solutions.- References.- Index.