On the distribution of the first exit time and overshoot in a two-sided boundary crossing problem

V. I. Lotov^ab, A. S. Tarasenko<sup>b

a</sup> Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: We consider a random walk generated by a sequence of independent identically distributed random variables. We assume that the distribution function of a jump of the random walk equals an exponential polynomial on the negative half-axis. For double transforms of the joint distribution of the first exit time from an interval and overshoot, we obtain explicit expressions depending on finitely many parameters that, in turn, we can derive from the system of linear equations. The principal difference of the present article from similar results in this direction is the rejection of using factorization components and projection operators connected with them.

Key words: random walk, two-sided boundary crossing problem, moment generating functions.

UDC: 519.21

Received: 24.12.2011

 English version: Siberian Advances in Mathematics, 2013, 23:2, 91–98

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