Markov Transition Functions and Semigroups of Measures

• DOI: 10.1007/s00233-006-0636-z
• Publication Date: 2006-12-13T18:22:06Z
• Authors: Timothy Lant; Horst R. Thieme
• Keywords: 0103 physical sciences; 01 natural sciences

The application of operator semigroups to Markov processes is extended to Markov transition functions which do not have the Feller property. Markov transition functions are characterized as solutions of forward and backward equations which involve the generators of integrated semigroups and are shown to induce integral semigroups on spaces of measures.