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 $t=0$.
Citation
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
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