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A stochastic differential equation with a sticky point. (English) Zbl 1291.60113

Summary: We consider a degenerate stochastic differential equation that has a sticky point in the Markov process sense. We prove that weak existence and weak uniqueness hold, but that pathwise uniqueness does not hold nor does a strong solution exist.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J60 Diffusion processes
60J65 Brownian motion
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