Electronic Journal of Probability

Boundary Conditions for One-Dimensional Biharmonic Pseudo Process

Kunio Nishioka

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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

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

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

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Zentralblatt MATH identifier

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

Boundary conditions for biharmonic pseudo process killing reflection stopping

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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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