Random times and multiplicative systems

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Li, Libo¹  Rutkowski, Marek¹ 

[1] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

关键词: Random time;    Azema supermartingale;    Multiplicative system;   

DOI  :  10.1016/j.spa.2012.02.011

来源: Elsevier

【 摘 要 】

The present research is motivated by the recent results of Jeanblanc and Song (2011) [10,11]. Our aim is to demonstrate, with the help of multiplicative systems introduced in Meyer (1979) [21], that for any given positive F-submartingale F such that F-infinity = 1. there exists a random time tau on some extension of the filtered probability space such that the Azema submartingale associated with tau coincides with F. Pertinent properties of this construction are studied and it is subsequently extended to the case of several correlated random times with the predetermined univariate conditional distributions. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free