Electronic Journal of Probability

Boundary Conditions for One-Dimensional Biharmonic Pseudo Process

Kunio Nishioka

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Abstract

We study boundary conditions for a stochastic pseudo processes corresponding to the biharmonic operator. The biharmonic pseudo process (BPP for short). is composed, in a sense, of two different particles, a monopole and a dipole. We show how an initial-boundary problems for a 4-th order parabolic differential equation can be represented by BPP with various boundary conditions for the two particles: killing, reflection and stopping.

Article information

Source
Electron. J. Probab., Volume 6 (2001), paper no. 13, 27 pp.

Dates
Accepted: 21 May 2001
First available in Project Euclid: 19 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1461097643

Digital Object Identifier
doi:10.1214/EJP.v6-86

Mathematical Reviews number (MathSciNet)
MR1844510

Zentralblatt MATH identifier
0978.60087

Subjects
Primary: 60J50: Boundary theory
Secondary: 35K35: Initial-boundary value problems for higher-order parabolic equations 60G18: Self-similar processes 60G20: Generalized stochastic processes 60J30

Keywords
Boundary conditions for biharmonic pseudo process killing reflection stopping

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Nishioka, Kunio. Boundary Conditions for One-Dimensional Biharmonic Pseudo Process. Electron. J. Probab. 6 (2001), paper no. 13, 27 pp. doi:10.1214/EJP.v6-86. https://projecteuclid.org/euclid.ejp/1461097643


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