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 Electronic Journal of Probability > Vol. 12 (2007) > Paper 11 open journal systems 


First hitting time and place, monopoles and multipoles for pseudo-processes driven by the equation ∂u/∂t =± ∂Nu/∂xN

Aimé Lachal, INSA de Lyon


Abstract
Consider the high-order heat-type equation ∂u/∂t =± ∂Nu/∂xN for an integer N>2 and introduce the related Markov pseudo-process (X(t))t≥ 0. In this paper, we study several functionals related to (X(t))t≥ 0: the maximum M(t) and minimum m(t) up to time t; the hitting times ta+ and ta- of the half lines (a,+∞) and (-∞,a) respectively. We provide explicit expressions for the distributions of the vectors (X(t),M(t)) and (X(t),m(t)), as well as those of the vectors (ta+,X(ta+)) and (ta-,X(ta-)).


Full text: PDF

Pages: 300-353

Published on: March 28, 2007
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Electronic Journal of Probability. ISSN: 1083-6489