Markov Processes, Feller Semigroups and Evolution Equations (Cartonné)

The book provides a systemic treatment of time-dependent strong Markov processes with values in a Polish space. It describes their 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 mathematical physics, hedging models in financial mathematics, and population or other models in which the Markov property plays a role.