This article is cited in 8 papers

Probability theory and mathematical statistics

Large deviation principle for multidimensional first compound renewal processes in the phase space

A. A. Mogulskii^ab, E. I. Prokopenko<sup>ba

a</sup> 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.

UDC: 519.21

MSC: 60K05, 60F10

Received June 4, 2019, published October 17, 2019

DOI: 10.33048/semi.2019.16.101

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