Martingale structure of Skorohod integral processes

• 成果类型: Article
• 署名作者: Peccati, Giovanni; Thieullen, Michele; Tudor, Ciprian A.
• 署名单位: Sorbonne Universite; Sorbonne Universite; Universite Paris Cite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000756
• 发表日期: 2006
• 页码: 1217-1239
• 关键词: stochastic calculus

摘要

Let the process {Y-t, t is an element of [0, 1]} have the form Y-t = delta(u1([o,t])), where delta stands for a Skorohod integral with respect to Brownian motion and u is a measurable process that verifies some suitable regularity conditions. We use a recent result by Tudor to prove that Y-t can be represented as the limit of linear combinations of processes that are products of forward and backward Brownian martingales. Such a result is a further step toward the connection between the theory of continuous-time (semi) martingales and that of anticipating stochastic integration. We establish an explicit link between our results and the classic characterization (owing to Due and Nualart) of the chaotic decomposition of Skorohod integral processes. We also explore the case of Skorohod integral processes that are time-reversed Brownian martingales and provide an anticipating counterpart to the classic optional sampling theorem for It (o) over cap stochastic integrals.