On purely discontinuous additive functionals of subordinate Brownian motions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Vondracek, Zoran¹  Wagner, Vanja¹ 

[1] Univ Zagreb, Fac Sci, Dept Math, Zagreb, Croatia

关键词: Additive functionals;    Subordinate Brownian motion;    Purely discontinuous Girsanov transform;    Absolute continuity;    Singularity;    Relative entropy;   

DOI  :  10.1016/j.spa.2017.06.003

来源: Elsevier

【 摘 要 】

Let A(t) = Es <= tF(Xs-, X-s) be a purely discontinuous additive functional of a subordinate Brownian motion X = (X-t, P-x). We give a sufficient condition on the non-negative function F that guarantees that finiteness of A(infinity) implies finiteness of its expectation. This result is then applied to study the relative entropy of P-x and the probability measure induced by a purely discontinuous Girsanov transform of the process X. We prove these results under the weak global scaling condition on the Laplace exponent of the underlying subordinator. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free