The 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. Contents: Introduction: Introduction: Stochastic Differential Equations; Strong Markov Processes: Strong Markov Processes on Polish Spaces; Strong Markov Processes: Proof of 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. | Markov Processes Feller Semigroups and Evolution Equations by Jan A Van Casteren, Hardcover | Indigo Chapters