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Construction and regularity of transition functions on polish spaces under measurability conditions

Construction and regularity of transition functions on polish spaces under measurability conditions This paper concerns the construction and regularity of a transition (probability) function of a non-homogeneous continuous-time Markov process with given transition rates and a general state space. Motivating from a lot of restriction in applications of a transition function with continuous (in t ≥ 0) and conservative transition rates q(t, x, Λ), we consider the case that q(t, x, Λ) are only required to satisfy a mild measurability (in t ≥ 0) condition, which is a generalization of the continuity condition. Under the measurability condition we construct a transition function with the given transition rates, provide a necessary and sufficient condition for it to be regular, and further obtain some interesting additional results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Construction and regularity of transition functions on polish spaces under measurability conditions

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Publisher
Springer Journals
Copyright
Copyright © 2013 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-013-0208-4
Publisher site
See Article on Publisher Site

Abstract

This paper concerns the construction and regularity of a transition (probability) function of a non-homogeneous continuous-time Markov process with given transition rates and a general state space. Motivating from a lot of restriction in applications of a transition function with continuous (in t ≥ 0) and conservative transition rates q(t, x, Λ), we consider the case that q(t, x, Λ) are only required to satisfy a mild measurability (in t ≥ 0) condition, which is a generalization of the continuity condition. Under the measurability condition we construct a transition function with the given transition rates, provide a necessary and sufficient condition for it to be regular, and further obtain some interesting additional results.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 20, 2013

References