Markov Processes, Feller Semigroups and Evolution Equations by Jan van Casteren
(Series on Concrete and Applicable Mathematics)

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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.

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Published November 25, 2010 by World Scientific Publishing Company. 824 pages
Genres: Science & Math.