Stochastic differential equations for Dirichlet processes
成果类型：
Article
署名作者：
Bass, RF; Chen, ZQ
署名单位：
University of Connecticut; University of Washington; University of Washington Seattle
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s004400100151
发表日期：
2001
页码：
422-446
关键词：
摘要：
We consider the stochastic differential equation dX(t) = a(X-t)dW(t) + b(X-t)dt, where W is a one-dimensional Brownian motion. We formulate the notion of solution and prove strong existence and pathwise uniqueness results when a is in C-1/2 and b is only a generalized function, for example, the distributional derivative of a Holder function or of a function of bounded variation. When b = aa', that is, when the generator of the SDE is the divergence form operator L = 1/2 d/dx (a(2) d/dx), a result on non-existence of a strong solution and non-pathwise uniqueness is given as well as a result which characterizes when a solution is a semimartingale or not. We also consider extensions of the notion of Stratonovich integral.