Degenerate stochastic differential equations and super-Markov chains

被引：39

作者：

Athreya, SR ^{[1
]}

Barlow, MT

Bass, R

Perkins, EA

机构：

[1] Indian Stat Inst, Stat Math Unit, New Delhi 110016, India

[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

[3] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2002年 / 123卷 / 04期

关键词：

stochastic differential equations; Martingale problem; elliptic operators; degenerate operators; diffusions; Bessel processes;

D O I：

10.1007/s004400100191

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider diffusions corresponding to the generator Lf(x) = Sigma(i=1)(d) x(i)gamma(i)(x) partial derivative(2)/partial derivativex(i)(2)f(x) + b(i)(x)partial derivative/partial derivativex(i) f(x), x is an element of R-+(d), for continuous gamma(i), b(i) : R-+(d) --> R with gamma(i) nonnegative. We show uniqueness for the corresponding martingale problem under certain non-degeneracy conditions on b(i), gamma(i) and present a counter-example when these conditions are not satisfied. As a special case, we establish uniqueness in law for some classes of super-Markov chains with state dependent branching rates and spatial motions.

引用

页码：484 / 520

页数：37