Functional limit theorems for renewal shot noise processes with increasing response functions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Iksanov, Alexander

关键词: Continuous mapping theorem;    fractionally integrated (inverse) stable process;    Functional limit theorem;    M-1 topology;    Renewal shot noise process;    Spectrally negative stable process;   

DOI  :  10.1016/j.spa.2013.01.019

来源: Elsevier

【 摘 要 】

We consider renewal shot noise processes with response functions which are eventually nondecreasing and regularly varying at infinity. We prove weak convergence of renewal shot noise processes, properly normalized and centered, in the space D[0, infinity) under the J(1) or M-1 topology. The limiting processes are either spectrally nonpositive stable Levy processes, including the Brownian motion, or inverse stable subordinators (when the response function is slowly varying), or fractionally integrated stable processes or fractionally integrated inverse stable subordinators (when the index of regular variation is positive). The proof exploits fine properties of renewal processes, distributional properties of stable Levy processes and the continuous mapping theorem. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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