2005/04/12 by Giovanni Peccati, Peccati, Giovanni, Ciprian A. Tudor +1
Economics, Econometrics and Finance · Mathematics · #60G51 #60H05 #60H07 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:60G51 #msc:60H05 #msc:60H07
paper · pdf · doi:10.48550/arxiv.math/0504244
Probability Theory
arxiv created 2005/04/12 · openalex publication_date 2005/04/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let N_t be a standard compensated Poisson process on [0,1]. We prove a new characterization of anticipating integrals of the Skorohod type with respect to N, and use it to obtain several counterparts to well established properties of semimartingale stochastic integrals. In particular we show that, if the integrand is sufficiently regular, anticipating Skorohod integral processes with respect to N admit a pointwise representation as usual Itô integrals in an independently enlarged filtration. We apply such a result to: (i) characterize Skorohod integral processes in terms of products of backward and forward Poisson martingales, (ii) develop a new Itô-type calculus for anticipating integrals on the Poisson space, and (iii) write Burkholder-type inequalities for Skorohod integrals.