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This article is cited in 9 scientific papers (total in 9 papers)
Probability theory and mathematical statistics
Large deviation principle for multidimensional first compound renewal processes in the phase space
A. A. Mogulskiiab, E. I. Prokopenkoba a Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
b Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
Abstract:
We obtain the large deviation principles for multidimensional first compound renewal processes $\mathbf{Z}(t)$ in the phase space $\mathbb{R}^d$, for this we find and investigate the rate function $D_Z(\alpha)$. Also we find asymptotics for the Laplace transform of this process when the time goes to infinity, for this we find and investigate the so-called fundamental function $A_Z(\mu)$.
Keywords:
compound multidimensional renewal process, large deviations, renewal measure, Cramer's condition, deviation (rate) function, second deviation (rate) function, fundamental function.
Received June 4, 2019, published October 17, 2019
Citation:
A. A. Mogulskii, E. I. Prokopenko, “Large deviation principle for multidimensional first compound renewal processes in the phase space”, Sib. Èlektron. Mat. Izv., 16 (2019), 1464–1477
Linking options:
https://www.mathnet.ru/eng/semr1142 https://www.mathnet.ru/eng/semr/v16/p1464
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