@article{Iksanov_Rashytov_2021, title={A functional limit theorem without centering for general shot noise processes}, volume={73}, url={http://umj.imath.kiev.ua/index.php/umj/article/view/6210}, DOI={10.37863/umzh.v73i2.6210}, abstractNote={<p>UDC 519.27</p> <p>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.<span class="Apple-converted-space"> </span>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.<span class="Apple-converted-space"> </span>We give several examples of particular counting processes satisfying the sufficient conditions and formulate the corresponding limit theorems.<span class="Apple-converted-space"> </span>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.</p>}, number={2}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Iksanov, A. and Rashytov , B.}, year={2021}, month={Feb.}, pages={160 - 178} }