Description
Book SynopsisInteractions between the theory of partial differential equations of elliptic and parabolic types and the theory of stochastic processes are beneficial for probability theory and analysis. This book shows connections between linear and semilinear differential equations and the corresponding Markov processes called diffusions and superdiffusions.
Table of ContentsIntroduction Parabolic equations and branching exit Markov systems: Linear parabolic equations and diffusions Branching exit Markov systems Superprocesses Semilinear parabolic equations and superdiffusions Elliptic equations and diffusions: Linear elliptic equations and diffusions Positive harmonic functions Moderate solutions of $Lu=\psi(u)$ Stochastic boundary values of solutions Rough trace Fine trace Martin capacity and classes $\mathcal{N}_1$ and $\mathcal{N}_0$ Null sets and polar sets Survey of related results Basic facts of Markov processes and Martingales Facts on elliptic differential equations Epilogue Bibliography Subject index Notation index.
