Let (X(t))t≥0 be the pseudo-process driven by the high-order heat-type equation ∂u = ± ∂Nu , ∂t ∂xN where N is an integer greater than 2. We consider the sojourn time spent by (X(t))t≥0 in [a,+∞) (a ∈ R), up to a fixed time t > 0: Ta(t) = 0t 1l[a,+∞)(X(s)) ds. The purpose of this paper is to explicit the joint pseudo-distribution of the vector (Ta(t),X(t)) when the pseudo-process starts at a point x ∈ R at time 0. The method consists in solving a boundary value problem satisfied by the Laplace transform of the aforementioned distribution.
Joint distribution of the process and its sojourn time in a half-line $[a,+\infty)$ for pseudo-processes driven by a high-order heat-type equation / Cammarota, Valentina; A., Lachal. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - STAMPA. - 122:(2012), pp. 217-249. [10.1016/j.spa.2011.08.004]
Joint distribution of the process and its sojourn time in a half-line $[a,+\infty)$ for pseudo-processes driven by a high-order heat-type equation.
CAMMAROTA, VALENTINAMembro del Collaboration Group
;
2012
Abstract
Let (X(t))t≥0 be the pseudo-process driven by the high-order heat-type equation ∂u = ± ∂Nu , ∂t ∂xN where N is an integer greater than 2. We consider the sojourn time spent by (X(t))t≥0 in [a,+∞) (a ∈ R), up to a fixed time t > 0: Ta(t) = 0t 1l[a,+∞)(X(s)) ds. The purpose of this paper is to explicit the joint pseudo-distribution of the vector (Ta(t),X(t)) when the pseudo-process starts at a point x ∈ R at time 0. The method consists in solving a boundary value problem satisfied by the Laplace transform of the aforementioned distribution.File | Dimensione | Formato | |
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