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Joint distribution of the process and its sojourn time on the positive half-line for pseudo-processes governed by high-order heat equation
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Aimé Lachal, INSA de Lyon
Valentina Cammarota, University of Rome La Sapienza
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Abstract
Consider the high-order heat-type equation ∂ u/∂
t=± ∂N u/∂ xN
for an integer N>2 and introduce
the related Markov pseudo-process (X(t))t≥ 0. In this paper,
we study the sojourn time T(t) in the interval [0,+∞) up to
a fixed time t for this pseudo-process. We provide explicit expressions for the joint distribution of the couple (T(t),X(t)).
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Full text: PDF
Pages: 895-931
Published on: June 17, 2010
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