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 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)).
Joint distribution of the process and its sojourn time on the positive half-line for pseudo-processes governed by high-order heat equation / Cammarota, Valentina; A., Lachal. - In: ELECTRONIC JOURNAL OF PROBABILITY. - ISSN 1083-6489. - ELETTRONICO. - 15:(2010), pp. 895-931. [10.1214/EJP.v15-782]
Joint distribution of the process and its sojourn time on the positive half-line for pseudo-processes governed by high-order heat equation.
CAMMAROTA, VALENTINAMembro del Collaboration Group
;
2010
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 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)).| File | Dimensione | Formato | |
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