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
NAKAJIMA, Tadashi ; SATO, Sadao
Tokyo J. of Math., Tome 22 (1999) no. 2, p. 399-413 / Harvested from Project Euclid
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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 $t=0$.
Publié le : 1999-12-15
Classification:  
@article{1270041446,
     author = {NAKAJIMA, Tadashi and SATO, Sadao},
     title = {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},
     journal = {Tokyo J. of Math.},
     volume = {22},
     number = {2},
     year = {1999},
     pages = { 399-413},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1270041446}
}

NAKAJIMA, Tadashi; SATO, Sadao. 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. of Math., Tome 22 (1999) no. 2, pp.  399-413. http://gdmltest.u-ga.fr/item/1270041446/