Record number :
108278
Title of article :
On Sojourn Distributions of Processes Related to Some Higher-Order Heat-Type Equations
Author/Authors :
Y. Nikitin، نويسنده , , E. Orsingher، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2000
Pages :
-996
From page :
997
To page :
0
Abstract :
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 thirdorder "process" but a different law emerges when the condition X(t)>0 is considered.
Keywords :
Feynman-Kac functional , arc-sine law , sojourn time , Laplace transform , higher order heat equations , airy function , Brownian motion
Journal title :
JOURNAL OF THEORETICAL PROBABILITY
Serial Year :
2000
Link To Document :
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