Optimal Approximation of Skorohod Integrals
نویسندگان
چکیده
منابع مشابه
Conditional Stein approximation for Itô and Skorohod integrals
We derive conditional Edgeworth-type expansions for Skorohod and Itô integrals with respect to Brownian motion, based on cumulant operators defined by the Malliavin calculus. As a consequence we obtain conditional Stein approximation bounds for multiple stochastic integrals and quadratic Brownian functionals.
متن کاملCentral limit theorems for multiple Skorohod integrals
In this paper, we prove a central limit theorem for a sequence of multiple Skorohod integrals using the techniques of Malliavin calculus. The convergence is stable, and the limit is a conditionally Gaussian random variable. Some applications to sequences of multiple stochastic integrals, and renormalized weighted quadratic variation of the fractional Brownian motion are discussed.
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Given an increasing function H : [0, 1) → [0,∞) and An(H) := inf τ∈Tn n X i=1 Z ti ti−1 (ti − t)H (t)dt ! 1 2 , where Tn := {τ = (ti) n i=0 : 0 = t0 < t1 < · · · < tn = 1}, we characterize the property An(H) ≤ c √ n , and give conditions for An(H) ≤ c √ nβ and An(H) ≥ 1 c √ nβ for β ∈ (0, 1), both in terms of integrability properties of H . These results are applied to the approximation of cert...
متن کاملStein approximation for Itô and Skorohod integrals by Edgeworth type expansions
We derive Edgeworth-type expansions for Skorohod and Itô integrals with respect to Brownian motion, based on cumulant operators defined by the Malliavin calculus. As a consequence we obtain Stein approximation bounds for stochastic integrals, which apply to SDE solutions and to multiple stochastic integrals.
متن کاملCumulant operators and moments of the Itô and Skorohod integrals
where the sum runs over the partitions B1, . . . , Ba of {1, . . . , n} with cardinal |Bi| by the Faà di Bruno formula, cf. [5], [6] and references therein for background on combinatorial probability. When X is centered Gaussian, e.g. X is the Wiener integral of a deterministic function with respect to a standard Brownian motion (Bt)t∈R+ , we have κ X n = 0, n 6= 2, and (1.1) reads as Wick’s th...
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ژورنال
عنوان ژورنال: Journal of Theoretical Probability
سال: 2016
ISSN: 0894-9840,1572-9230
DOI: 10.1007/s10959-016-0716-2