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Boundary conditions for one-dimensional biharmonic pseudo process. (English) Zbl 0978.60087

Summary: We study boundary conditions for a stochastic pseudo-process 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 problem for a 4th order parabolic differential equation can be represented by BPP with various boundary conditions for the two particles: killing, reflection and stopping.

MSC:

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