This article is cited in 9 papers

Probability theory and mathematical statistics

The rate function and the fundamental function for multidimensional compound renewal process

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 consider two multidimensional compound renewal processes $\mathbf{Z}(t)$ and $\mathbf{Y}(t)$. Assuming that the increments satisfy the Cramer's condition, we define and investigate the rate functions and the fundamental functions for the processes $\mathbf{Z}(t)$ and $\mathbf{Y}(t)$.

Keywords: compound multidimensional renewal process, large deviations, Cramer's condition, deviation (rate) function, fundamental function, Legendre transformation.

UDC: 519.21

MSC: 60K05, 60F10

Received June 4, 2019, published October 17, 2019

DOI: 10.33048/semi.2019.19.100

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