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Absolute continuity/singularity and relative entropy properties for probability measures induced by diffusions on infinite time intervals

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  • Ben-Ari, Iddo
  • Pinsky, Ross G.

Abstract

In this paper we study mutual absolute continuity, finiteness of relative entropy and the possibility of their equivalence for probability measures on C([0,[infinity]);Rd) induced by diffusion processes. We also determine explicit events which distinguish between two mutually singular measures in certain one-dimensional cases.

Suggested Citation

  • Ben-Ari, Iddo & Pinsky, Ross G., 2005. "Absolute continuity/singularity and relative entropy properties for probability measures induced by diffusions on infinite time intervals," Stochastic Processes and their Applications, Elsevier, vol. 115(2), pages 179-206, February.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:2:p:179-206
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    Cited by:

    1. Vondraček, Zoran & Wagner, Vanja, 2018. "On purely discontinuous additive functionals of subordinate Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 707-725.
    2. Mishura, Yuliya & Yoshidae, Nakahiro, 2022. "Divergence of an integral of a process with small ball estimate," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 1-24.

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