Product of two multiple stochastic integralswith respect to a normal
نویسنده
چکیده
Let M be a normal martingale (i.e. < M; M > (t) = t), we decompose the product of two multiple stochastic integrals (with respect to M) I n (f)I m (g) as a sum of n^m terms H k. H k is equal to the integral over R k + of the function t ! I n+m?2k (h k (t; :)), with respect to the k-tensor product of dM; M]:; h k being an explicit function depending only on f and g. Our formula generalizes the well-known result concerning Brownian motion and compensated Poisson process and allows us to improve some results of Emery related to the chaos representation property of solution of the structure equation.
منابع مشابه
Product of two multiple stochastic integrals with respect to a normal martingale
Let M be a normal martingale i.e. M ; M t = t, we decompose the product of two m ultiple stochastic integrals with respect to M I n fI m g as a sum of n^m terms H k. H k is equal to the integral over R k + of the function t ! I n+m,2k h k t; :, with respect to the k-tensor product of dM;M:; h k being an explicit function depending only on f and g. Our formula generalizes the well-known result c...
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