Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155882 | Stochastic Processes and their Applications | 2012 | 33 Pages |
Abstract
Let (X(t))t≥0(X(t))t≥0 be the pseudo-process driven by the high-order heat-type equation ∂u∂t=±∂Nu∂xN, where NN is an integer greater than 2. We consider the sojourn time spent by (X(t))t≥0(X(t))t≥0 in [a,+∞)[a,+∞) (a∈Ra∈R), up to a fixed time t>0t>0: Ta(t)=∫0t1[a,+∞)(X(s))ds. The purpose of this paper is to provide an explicit expression for the joint pseudo-distribution of the vector (Ta(t),X(t))(Ta(t),X(t)) when the pseudo-process starts at a point x∈Rx∈R at time 00. The method consists in solving a boundary value problem satisfied by the Laplace transform of the aforementioned distribution.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Valentina Cammarota, Aimé Lachal,