Description
Book SynopsisThe book provides a systemic treatment of time-dependent strong Markov processes with values in a Polish space. It describes its generators and the link with stochastic differential equations in infinite dimensions. In a unifying way, where the square gradient operator is employed, new results for backward stochastic differential equations and long-time behavior are discussed in depth. The book also establishes a link between propagators or evolution families with the Feller property and time-inhomogeneous Markov processes. This mathematical material finds its applications in several branches of the scientific world, among which are mathematical physics, hedging models in financial mathematics, and population models.
Table of ContentsIntroduction: Introduction: Stochastic Differential Equations; Strong Markov Processes: Strong Markov Processes on Polish Spaces; Strong Markov Processes: Proof on Main Results; Space-Time Operators and Miscellaneous Topics; Backward Stochastic Differential Equations: Feynman-Kac Formulas, Backward Stochastic Differential Equations and Markov Processes; Viscosity Solutions, Backward Stochastic Differential Equations and Markov Processes; The Hamilton-Jacobi-Bellman Equation and the Stochastic Noether Theorem; Long Time Behavior: On Non-Stationary Markov Processes and Dunford Projections; Coupling Methods and Sobolev Type Inequalities; Invariant Measure.
