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December 1999 On the Joint Distribution of the First Hitting Time and the First Hitting Place to the Space-Time Wedge Domain of a Biharmonic Pseudo Process
Tadashi NAKAJIMA, Sadao SATO
Tokyo J. Math. 22(2): 399-413 (December 1999). DOI: 10.3836/tjm/1270041446

Abstract

We consider the equation \[ \frac{\partial u}{\partial t}(t,x)=-\Delta^{2}u(t,x) \] for the biharmonic operator $-\Delta^2$. We define the pseudo process corresponding to this equation as Nishioka's sense. We obtain the Laplace-Fourier transform of the joint distribution of the first hitting time $\tau(\omega)=\inf\{t>0:\omega(t)<\alpha t-a\}$ $(a>0, \alpha\in\mathbf{R})$ and the first hitting place $\omega(\tau)$, where each path $\omega(t)$ starts from 0 at $t=0$.

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Tadashi NAKAJIMA. Sadao SATO. "On the Joint Distribution of the First Hitting Time and the First Hitting Place to the Space-Time Wedge Domain of a Biharmonic Pseudo Process." Tokyo J. Math. 22 (2) 399 - 413, December 1999. https://doi.org/10.3836/tjm/1270041446

Information

Published: December 1999
First available in Project Euclid: 31 March 2010

zbMATH: 0952.35061
MathSciNet: MR1727883
Digital Object Identifier: 10.3836/tjm/1270041446

Rights: Copyright © 1999 Publication Committee for the Tokyo Journal of Mathematics

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Vol.22 • No. 2 • December 1999
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