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JOURNALS // Teoriya Veroyatnostei i ee Primeneniya // Archive

Teor. Veroyatnost. i Primenen., 2000 Volume 45, Issue 1, Pages 166–175 (Mi tvp330)

This article is cited in 2 papers

Short Communications

A random walk with a skip-free component and the Lagrange inversion formula

O. V. Viskov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The paper shows that for a random walk with a skip-free component, distributions of certain first passage times and hitting points are infinitely divisible. The proofs are elementary and based on an algebraic approach to the classical Lagrange formula. This approach permits us to write explicitly the respective Levy measures.

Keywords: Lagrange inversion formula, Heisenberg–Weyl algebra, infinitely divisible distributions, skip-free random walks.

Received: 09.07.1999

DOI: 10.4213/tvp330


 English version:
Theory of Probability and its Applications, 2001, 45:1, 164–172

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