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.
"Boundary Conditions for One-Dimensional Biharmonic Pseudo Process." Electron. J. Probab. 6 1 - 27, 2001. https://doi.org/10.1214/EJP.v6-86