Product of two multiple stochastic integrals with respect to a normal martingale
type: Item
instance of: scholarly article
title: Product of two multiple stochastic integrals with respect to a normal martingale
zbMATH Open document ID: 0946.60033
DOI: 10.1016/S0304-4149(97)00101-4
author: Francesco Russo
author: Pierre Vallois
published in: Stochastic Processes and their Applications
publication date: 2000-03-01T00:00:00Z
review text: Let \(I_n(g)\) and \(I_m(f)\) be two multiple stochastic integrals with respect to a normal martingale \(M\), where \(g\) and \(f\) are symmetric, square integrable functions on \(R^n_+\) and \(R^m_+\), respectively. The product \(I_n(g)I_m(f)\) is decomposed as a sum of \(n\land m\) terms \(H_k\) where \(H_k\) is the integral over \(R^k_+\) of the function \(t\to I_{n+m-2k}(h_k(t,.))\), with respect to the \(k\)-tensor product of \(d[M,M]\), \(h_k\) being an explicit function depending only on \(g\) and \(f\). This extends some earlier results achieved for the cases when \(M\) is a Brownian motion or a compensated Poisson process.
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 1409163
zbMATH Keywords: normal martingale
zbMATH Keywords: multiple stochastic integral
zbMATH Keywords: chaos representation property
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1409163