Measurability of semimartingale characteristics with respect to the probability law

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:124

Article

Neufeld, Ariel¹  Nutz, Marcel² 

[1] ETH, Dept Math, Zurich, Switzerland

[2] Columbia Univ, Dept Math, New York, NY 10027 USA

关键词: Semimartingale characteristics;    Semimartingale property;    Doob-Meyer decomposition;   

DOI  :  10.1016/j.spa.2014.07.006

来源: Elsevier

【 摘 要 】

Given a cadlag process X on a filtered measurable space, we construct a version of its semimartingale characteristics which is measurable with respect to the underlying probability law. More precisely, let B-sem be the set of all probability measures P under which X is a semimartingale. We construct processes (B-P,C, v(P)) which are jointly measurable in time, space, and the probability law P, and are versions of the semimartingale characteristics of X under P for each P is an element of B-sem. This result gives a general and unifying answer to measurability questions that arise in the context of quasi-sure analysis and stochastic control under the weak formulation. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free