Green formulas in anticipating stochastic calculus
نویسندگان
چکیده
منابع مشابه
Stochastic Calculus with Anticipating Integrands
We study the stochastic integral defined by Skorohod in [24] of a possibly anticipating integrand, as a function of its upper limit, and establish an extended It6 formula. We also introduce an extension of Stratonovich's integral, and establish the associated chain rule. In all the results, the adaptedness of the integrand is replaced by a certain smoothness requirement.
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In this paper, we establish the existence of the solutions (X,L) of reflected stochastic differential equations with possible anticipating initial random variables. The key is to obtain some substitution formula for Stratonovich integrals via a uniform convergence of the corresponding Riemann sums.
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Rn×Rn S( x+ y 2 , η) e2iπ〈x−y, η〉 u(y) dy dη : such a linear operator extends as a continuous operator from S ′(Rn) to S(R) while, in the case when S ∈ S ′(Rn ×R) , one can still define Op(S) as a linear operator from S(R) to S ′(Rn) ; also, Op sets up an isometry from L(R×R) onto the space of Hilbert-Schmidt operators on L(R) . The sharp composition S1#S2 of two symbols, say lying in S(R×R) , ...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1995
ISSN: 0304-4149
DOI: 10.1016/0304-4149(94)00070-a