On the Independence of Multiple Stochastic Integrals With Respect to a Class of Martingales
نویسنده
چکیده
Abstract We study via the chaotic calculus the independence of multiple stochastic integrals In(fn), Im(gm) with respect to martingales (Mt)t∈IR+ that satisfy a deterministic structure equation. It is shown that if the integrals are independent and if a contraction denoted as fn ◦1 gm does not vanish on A ∈ B(IR+), a.e., then the stochastic measure associated to (Mt)t∈IR+ is Gaussian on A. In the Poisson case, In(fn), Im(gm) are independent if and only if fn ◦1 gm vanishes a.e.
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