Limit theorems for non-Markovian marked dynamic contagion processes

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Yao, Nian¹  Xiao, Mingqing² 

[1] Shenzhen Univ, Coll Math & Stat, Shenzhen 518060, Peoples R China

[2] Southern Illinois Univ, Dept Math, Carbondale, IL 62901 USA

关键词: Large deviation;    Central limit theorem;    Extreme values;    Point processes;   

DOI  :  10.1016/j.jmaa.2018.04.039

来源: Elsevier

【 摘 要 】

In this paper, we study a general dynamic contagion process that includes several standard point processes as special cases. We have developed (i) the corresponding large deviation principle; (ii) the corresponding law of large numbers; (iii) the corresponding central limit theorem, all of which are critical in describing the essential of this type of processes, and are not available in current literature. The proposed model provides a broader framework in the study of contagion processes in various applications. In particular, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for the risk model with marked dynamic contagion claim arrivals as an application. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free