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This 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. This mathematical material finds its applications in several branches of the scientific world among which mathematical physics, hedging models in financial mathematics, population models.

Markov processes. --- Semigroups of operators. --- Evolution equations. --- Evolutionary equations --- Equations, Evolution --- Equations of evolution --- Differential equations --- Operators, Semigroups of --- Operator theory --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes