Summary
LetL be a second-order partial differential operator inR d. LetR d be the finite union of disjoint polyhedra. Suppose that the diffusion matrix is everywhere non singular and constant on each polyhedron, and that the drift coefficient is bounded and measurable. We show that the martingale problem associated withL is well-posed.
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References
Blumenthal, R.M., Getoor, R.K.: Markov processes and potential theory. New York: Academic Press 1968
Ikeda, N., Watanabe, S.: Stochastic differential equations and diffusion processes. Tokyo: North-Holland/Kodansha 1981
Krein, M.G., Rutman, M.A.: Linear operators leaving invariant a cone in a Banach space. Am. Math. Soc. Selected Translations. Series 1, 10, 199–325 (1962)
Krylov, N.V., Safonov, M.V.: An estimate of the probability that a diffusion process hits a set of positive measure. Soviet Math. Dokl.20, 253–255 (1979)
Pardoux, E., Savona, C.: Piecewise linear filtering. Proceedings of an IMA meeting. Minneapolis (1986), to appear
Stroock, D.W., Varadham, S.R.S.: Multidimensional diffusion processes. Berlin Heidelberg New York: Springer 1979
Varadhan, S.R.S., Williams, R.J.: Brownian motion in a wedge with oblique reflection. Commun. Pure Appl. Math.38, 405–443 (1985)
Williams, R.J.: Brownian motion with polar drift. Trans. Am. Math. Soc.292, 225–246 (1985)
Krylov, N.V.: An inequality in the theory of stochastic integrals. Theor. Probab. Appl.16, 438–448 (1971)
Meyer, P.-A.. Un cours sur les intégrales stochastiques. Séminaire de Probabilités X. Berlin Heidelberg New York. Springer 1976
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The research of this author was partly supported by NSF Grant DMS 8500581
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Bass, R.F., Pardoux, E. Uniqueness for diffusions with piecewise constant coefficients. Probab. Th. Rel. Fields 76, 557–572 (1987). https://doi.org/10.1007/BF00960074
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DOI: https://doi.org/10.1007/BF00960074