## Kyoto Journal of Mathematics

- Kyoto J. Math.
- Volume 54, Number 3 (2014), 507-528.

### An approach to the pseudoprocess driven by the equation $\frac{\partial}{\partial t}=-A\frac{{\partial}^{3}}{\partial {x}^{3}}$ by a random walk

Tadashi Nakajima and Sadao Sato

#### Abstract

In this paper we study the pseudoprocess driven by ${\partial}_{t}=-A{\partial}_{x}^{3}$. Our method is an approximation by the pseudo–random walk. We obtain their joint distribution of the first hitting time and the first hitting place. In addition, this result is provided by the alternate method of Shimoyama.

#### Article information

**Source**

Kyoto J. Math., Volume 54, Number 3 (2014), 507-528.

**Dates**

First available in Project Euclid: 14 August 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.kjm/1408020875

**Digital Object Identifier**

doi:10.1215/21562261-2693415

**Mathematical Reviews number (MathSciNet)**

MR3263549

**Zentralblatt MATH identifier**

1303.13001

**Subjects**

Primary: 60G20: Generalized stochastic processes

Secondary: 35K35: Initial-boundary value problems for higher-order parabolic equations

#### Citation

Nakajima, Tadashi; Sato, Sadao. An approach to the pseudoprocess driven by the equation $\frac{\partial}{\partial t}=-A\frac{\partial^{3}}{\partial x^{3}}$ by a random walk. Kyoto J. Math. 54 (2014), no. 3, 507--528. doi:10.1215/21562261-2693415. https://projecteuclid.org/euclid.kjm/1408020875