Smooth densities for degenerate stochastic delay equations with hereditary drift
成果类型：
Article
署名作者：
Bell, DR; Mohammed, SEA
署名单位：
Southern Illinois University System; Southern Illinois University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176987807
发表日期：
1995
页码：
1875-1894
关键词：
摘要：
We establish the existence of smooth densities for solutions of Rd-valued stochastic hereditary differential systems of the form dx(t) = H(t, x) dt + g(t, x(t - r)) dW(t). In the above equation, W is an n-dimensional Wiener process, r is a positive time delay, H is a nonanticipating functional defined on the space of paths in R(d) and g is an n X d matrix-valued function defined on [0, infinity) X R(d), such that gg* has degeneracies of polynomial order on a hypersurface in R(d). In the course of proving this result, we establish a very general criterion for the hypoellipticity of a class of degenerate parabolic second-order time-dependent differential operators with space-independent principal part.