TY - JOUR

T1 - Conditional sojourn distributions of "processes" related to the third-order and fourth-order heat-type equations

AU - Nikitin, Y.

AU - Orsingher, E.

PY - 2000

Y1 - 2000

N2 - It is well known that the sojourn time of Brownian motion B(t), t>0 on the positive half-line, during the interval [0,t] and under the condition B(t)=0, is uniformly distributed, while it has the form of the "corrected arc-sine law" when the condition B(t)>0 is assumed. We find the analogues of these laws for "processes" X(t), t>0 governed by signed measures whose densities are the fundamental solutions of third and fourth-order heat-type equations. Surprisingly, both laws hold for the fourth-order "process." The uniform law is still valid for the third-order "process" but a different law emerges when the condition X(t)>0 is considered.

AB - It is well known that the sojourn time of Brownian motion B(t), t>0 on the positive half-line, during the interval [0,t] and under the condition B(t)=0, is uniformly distributed, while it has the form of the "corrected arc-sine law" when the condition B(t)>0 is assumed. We find the analogues of these laws for "processes" X(t), t>0 governed by signed measures whose densities are the fundamental solutions of third and fourth-order heat-type equations. Surprisingly, both laws hold for the fourth-order "process." The uniform law is still valid for the third-order "process" but a different law emerges when the condition X(t)>0 is considered.

M3 - Article

SP - 997

EP - 1012

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

SN - 0894-9840

IS - 4

ER -