Degenerate stochastic differential equations with Hölder continuous coefficients and super-Markov chains
Richard F. Bass and Edwin A. Perkins
Trans. Amer. Math. Soc. 355 (2003), 373-405
September 6, 2002
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Abstract: We consider the operator
acting on functions in . We prove uniqueness of the martingale problem for this degenerate operator under suitable nonnegativity and regularity conditions on and . In contrast to previous work, the need only be nonnegative on the boundary rather than strictly positive, at the expense of the and being Hölder continuous. Applications to super-Markov chains are given. The proof follows Stroock and Varadhan's perturbation argument, but the underlying function space is now a weighted Hölder space and each component of the constant coefficient process being perturbed is the square of a Bessel process.
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Richard F. Bass
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Edwin A. Perkins
Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada V6T 1Z2
Stochastic differential equations,
Received by editor(s):
February 1, 2002
Received by editor(s) in revised form:
June 6, 2002
September 6, 2002
The first author’s research was supported in part by NSF grant DMS9988496
The second author’s research was supported in part by an NSERC grant
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