A functional limit theorem without centering for general shot noise processes

Keywords: counting process; general shot noise process; Holder continuity; weak convergence in the Skorokhod space


UDC 519.27

We define a general shot noise process as the convolution of a deterministic càdlàg function and a locally finite counting process concentrated on the nonnegative halfline. In this paper, we provide the sufficient conditions ensuring that a general shot noise process properly normalized without centering converges weakly in the Skorokhod space. We give several examples of particular counting processes satisfying the sufficient conditions and formulate the corresponding limit theorems. The present work continues the investigation initiated in [Iksanov and Rashytov (2020)], where a functional limit theorem with centering was proved under the condition that the limit process is a Riemann–Liouville-type (Gaussian) process.


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How to Cite
Iksanov, A., and B. Rashytov. “A Functional Limit Theorem Without Centering for General Shot Noise Processes”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 2, Feb. 2021, pp. 160 -78, doi:10.37863/umzh.v73i2.6210.
Research articles