On stochastic differential equations driven by a Cauchy process and other stable Levy motions
成果类型：
Article
署名作者：
Zanzotto, PA
署名单位：
University of Udine
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
2002
页码：
802-825
关键词：
摘要：
We consider the class of one-dimensional stochastic differential equations d X-t = b(X-t-) dZ(t), t > 0, where b is a Beret measurable real function and Z is a strictly alpha-stable Levy process (0 < alpha < 2). Weak solutions are investigated improving previous results of the author in various ways. In particular, for the equation driven by a strictly 1-stable Levy process, a sufficient existence condition is proven. Also we extend the weak existence and uniqueness exact criteria due to Engelbert and Schmidt for the Brownian case (i.e., alpha = 2) to the class of equations with a such that 1 < alpha less than or equal to 2. The results employ some representation properties with respect to strictly stable Levy processes.