Skorohod and Stratonovich line integrals in the plane
نویسندگان
چکیده
منابع مشابه
The Geometry of Iterated Stratonovich Integrals
We give a summary on the geometry of iterated Stratonovich integrals. For this exposition, we always have the connection to stochastic Taylor expansion in mind. In particular, we believe that “cubature on Wiener space” is best understood in the setting presented in this text. Besides cubature on Wiener space, we also give a second application regarding the heat kernel on nilpotent free Lie groups.
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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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Formulae connecting the multiple Stratonovich integrals with single Ogawa and Stratonovich integrals are derived. Multiple Riemann-Stieltjes integrals with respect to certain smooth approximations of the Wiener process are considered and it is shown that these integrals converge to multiple Stratonovich integrals as the approximation converges to the Wiener process.
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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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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.
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1991
ISSN: 0304-4149
DOI: 10.1016/0304-4149(91)90081-m