## Tokyo Journal of Mathematics

- Tokyo J. Math.
- Volume 22, Number 2 (1999), 399-413.

### 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 and Sadao SATO

#### 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 $t=0$.

#### Article information

**Source**

Tokyo J. Math., Volume 22, Number 2 (1999), 399-413.

**Dates**

First available in Project Euclid: 31 March 2010

**Permanent link to this document**

https://projecteuclid.org/euclid.tjm/1270041446

**Digital Object Identifier**

doi:10.3836/tjm/1270041446

**Mathematical Reviews number (MathSciNet)**

MR1727883

**Zentralblatt MATH identifier**

0952.35061

#### Citation

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. Math. 22 (1999), no. 2, 399--413. doi:10.3836/tjm/1270041446. https://projecteuclid.org/euclid.tjm/1270041446