EXISTENCE AND CONTINUITY OF OCCUPATION DENSITIES OF STOCHASTIC INTEGRAL PROCESSES

• 成果类型: Article
• 署名作者: IMKELLER, P
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989282
• 发表日期: 1993
• 页码: 1050-1072
• 关键词: differential-equations

摘要

Let f be a square-integrable function on the unit square. Assume that the singular numbers (a(i))i is-an-element-of N of the Hilbert-Schmidt operator associated with f admit some 0 < alpha < 1/3 such that SIGMA(i = 1)infinity \alpha(i)\alpha < infinity. We present a purely stochastic method to investigate the occupation densities of the Skorohod integral process U induced by f. It allows us to show that U possesses continuous square-integrable occupation densities and obviously generalizes beyond the second Wiener chaos.