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- catalog abstract "This is author-approved bcc: This book discusses the interplay of diffusion processes and partial differential equations with an emphasis on probabilistic methods in PDE. It begins with stochastic differential equations, the probabilistic machinery needed to study PDE. After spending three chapters on probabilistic representations of solutions for PDE, regularity of solutions and one dimensional diffusions, the author discusses in depth two main types of second order linear differential operators: non-divergence operators and divergence operators, including topics such as the Harnack inequality of Krylov-Safonov for non-divergence operators and heat kernel estimates for divergence form operators. Martingale problems and the Malliavin calculus are presented in two other chapters. This book can be used as a textbook for a graduate course on diffusion theory with applications to PDE. It will also be a valuable reference to researchers in probability who are interested in PDE as well as for analysts who are interested in probabilistic methods. Richard F. Bass is Professor of Mathematics at the University of Washington. He has written many research papers on the topics covered by this book. Also Available: Richard F. Bass, Probabilistic Techniques in Analysis. Springer-Verlag New York, Inc, 0-387-94387-0".
- catalog contributor b10667942.
- catalog created "c1998.".
- catalog date "1998".
- catalog date "c1998.".
- catalog dateCopyrighted "c1998.".
- catalog description "Includes bibliographical references (p. [223]-228) and index.".
- catalog description "Stochastic Differential Equations -- Representations of Solutions -- Regularity of Solutions -- One Dimensional Diffusions -- Nondivergence Form Operators -- Martingale Problems -- Divergence Form Operators -- The Malliavin Calculus.".
- catalog description "This is author-approved bcc: This book discusses the interplay of diffusion processes and partial differential equations with an emphasis on probabilistic methods in PDE. It begins with stochastic differential equations, the probabilistic machinery needed to study PDE. After spending three chapters on probabilistic representations of solutions for PDE, regularity of solutions and one dimensional diffusions, the author discusses in depth two main types of second order linear differential operators: non-divergence operators and divergence operators, including topics such as the Harnack inequality of Krylov-Safonov for non-divergence operators and heat kernel estimates for divergence form operators. Martingale problems and the Malliavin calculus are presented in two other chapters. This book can be used as a textbook for a graduate course on diffusion theory with applications to PDE. It will also be a valuable reference to researchers in probability who are interested in PDE as well as for analysts who are interested in probabilistic methods. Richard F. Bass is Professor of Mathematics at the University of Washington. He has written many research papers on the topics covered by this book. Also Available: Richard F. Bass, Probabilistic Techniques in Analysis. Springer-Verlag New York, Inc, 0-387-94387-0".
- catalog extent "xiii, 232 p. :".
- catalog identifier "0387983155 (hardcover : alk. paper)".
- catalog isPartOf "Probability and its applications".
- catalog issued "1998".
- catalog issued "c1998.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "519.2 21".
- catalog subject "Diffusion processes.".
- catalog subject "Distribution (Probability theory).".
- catalog subject "Elliptic operators.".
- catalog subject "Global analysis (Mathematics).".
- catalog subject "Mathematics.".
- catalog subject "QA377 .B293 1998".
- catalog subject "Stochastic differential equations Numerical solutions.".
- catalog tableOfContents "Stochastic Differential Equations -- Representations of Solutions -- Regularity of Solutions -- One Dimensional Diffusions -- Nondivergence Form Operators -- Martingale Problems -- Divergence Form Operators -- The Malliavin Calculus.".
- catalog title "Diffusions and elliptic operators / Richard F. Bass.".
- catalog type "text".