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May 2006 Martingale structure of Skorohod integral processes
Giovanni Peccati, Michèle Thieullen, Ciprian A. Tudor
Ann. Probab. 34(3): 1217-1239 (May 2006). DOI: 10.1214/009117905000000756


Let the process {Yt,t∈[0,1]} have the form Yt=δ(u1[0,t]), where δ 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 Yt 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 Duc 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 Itô stochastic integrals.


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Giovanni Peccati. Michèle Thieullen. Ciprian A. Tudor. "Martingale structure of Skorohod integral processes." Ann. Probab. 34 (3) 1217 - 1239, May 2006.


Published: May 2006
First available in Project Euclid: 27 June 2006

zbMATH: 1134.60039
MathSciNet: MR2243882
Digital Object Identifier: 10.1214/009117905000000756

Primary: 60G15 , 60G40 , 60G44 , 60H05 , 60H07

Keywords: anticipating stochastic integration , Malliavin calculus , Martingale theory , stopping times

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 3 • May 2006
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