Degenerate stochastic differential equations with Hölder continuous coefficients and super-Markov chains期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Degenerate stochastic differential equations with Hölder continuous coefficients and super-Markov chains

Authors:	Richard F. Bass Edwin A. Perkins

Affiliation:	Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269 ; Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada V6T 1Z2

Abstract:	We consider the operator $begin{displaymath}sum_{i,j=1}^d sqrt{x_ix_j}gamma_{ij}(x) frac{partial^2}... ...partial x_j}+sum_{i=1}^d b_i(x) frac{partial}{partial x_i}end{displaymath}$ acting on functions in $C_b^2(mathbb{R}^d_+)$ . We prove uniqueness of the martingale problem for this degenerate operator under suitable nonnegativity and regularity conditions on $gamma_{ij}$ and . In contrast to previous work, the need only be nonnegative on the boundary rather than strictly positive, at the expense of the $gamma_{ij}$ 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.

Keywords:	Stochastic differential equations, margingale problem, elliptic operators, degenerate operators, diffusions, Bessel processes, superprocesses, H" older norms

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