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Zbl 0561.60082
Graham, Carl
Boundary processes: the calculus of processes diffusing on the boundary. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 21, 73-102 (1985). ISSN 0246-0203

The author extends some results obtained in the paper reviewed above, Zbl 0561.60081, which discuss the regularity of the transition probabilities of the boundary process of a reflecting diffusion process, to the case where the process diffuses on the boundary. Using the Malliavin calculus it is shown that the regularity is related to the degree of degeneracy at the boundary of the diffusion operators. The author establishes that there is interaction between the operator acting in the domain and the one on the boundary.
[R.J.Elliott]

MSC 2000:: *60J60 Diffusion processes
60J35 Transition functions
60G44 Martingales with continuous parameter
65H10 Systems of nonlinear equations (numerical methods)

Keywords: regularity of the transition probabilities of the boundary process; reflecting diffusion process; Malliavin calculus

Citations: Zbl 0561.60081

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