In this paper, we use a white noise approach to Malliavin calculus to prove the generalization of the Clark-Ocone formula , where E[F] denotes the generalized expectation, is the (generalized) Malliavin derivative, &a...In this paper, we use a white noise approach to Malliavin calculus to prove the generalization of the Clark-Ocone formula , where E[F] denotes the generalized expectation, is the (generalized) Malliavin derivative, ◊?is the Wick product and W(t) is the 1-dimensional Gaussian white noise.展开更多
In this article, exact solutions of Wick-type stochastic Kudryashov–Sinelshchikov equation have been obtained by using improved Sub-equation method. We have used Hermite transform for transforming the Wick-type stoch...In this article, exact solutions of Wick-type stochastic Kudryashov–Sinelshchikov equation have been obtained by using improved Sub-equation method. We have used Hermite transform for transforming the Wick-type stochastic Kudryashov–Sinelshchikov equation to deterministic partial differential equation. Also we have applied inverse Hermite transform for obtaining a set of stochastic solutions in the white noise space.展开更多
This paper surveys some results on Wick product and Wick renormalization. The framework is the abstract Wiener space. Some known results on Wick product and Wick renormalization in the white noise analysis framework a...This paper surveys some results on Wick product and Wick renormalization. The framework is the abstract Wiener space. Some known results on Wick product and Wick renormalization in the white noise analysis framework are presented for classical random variables. Some conditions are described for random variables whose Wick product or whose renormalization are integrable random variables. Relevant results on multiple Wiener integrals, second quantization operator, Malliavin calculus and their relations with the Wick product and Wick renormalization are also briefly presented. A useful tool for Wick product is the S-transform which is also described without the introduction of generalized random variables.展开更多
In this short note, we show that it is more natural to look the fractional Brownian motion as functionals of the standard white noises, and the fractional white noise calculus developed by Hu and Фksendal follows dir...In this short note, we show that it is more natural to look the fractional Brownian motion as functionals of the standard white noises, and the fractional white noise calculus developed by Hu and Фksendal follows directly from the classical white noise functional calculus. As examples we prove that the fractional Girsanov formula, the Ito type integrals and the fractional Black-Scholes formula are easy consequences of their classical counterparts. An extension to the fractional Brownian sheet is also briefly discussed.展开更多
Fundamental properties of Wick product of generalized operators are investigated. The annihilation and creation algebras are characterized from various points of view. Wick ordering widely used in quantum physics is i...Fundamental properties of Wick product of generalized operators are investigated. The annihilation and creation algebras are characterized from various points of view. Wick ordering widely used in quantum physics is interpreted as the Wick product of generalized operators.展开更多
文摘In this paper, we use a white noise approach to Malliavin calculus to prove the generalization of the Clark-Ocone formula , where E[F] denotes the generalized expectation, is the (generalized) Malliavin derivative, ◊?is the Wick product and W(t) is the 1-dimensional Gaussian white noise.
文摘In this article, exact solutions of Wick-type stochastic Kudryashov–Sinelshchikov equation have been obtained by using improved Sub-equation method. We have used Hermite transform for transforming the Wick-type stochastic Kudryashov–Sinelshchikov equation to deterministic partial differential equation. Also we have applied inverse Hermite transform for obtaining a set of stochastic solutions in the white noise space.
基金supported in part by the National Science Foundation under Grant No.DMS0504783the International Research Team on Complex Systems,Chines Academy of Sciences+2 种基金supported by the National Natural Science Foundation of China(No.10571167)the NationalBasic Research Program of China(973 Program)(No.2007CB814902)the Science Fund for CreativeResearch Groups(No.10721101)
文摘This paper surveys some results on Wick product and Wick renormalization. The framework is the abstract Wiener space. Some known results on Wick product and Wick renormalization in the white noise analysis framework are presented for classical random variables. Some conditions are described for random variables whose Wick product or whose renormalization are integrable random variables. Relevant results on multiple Wiener integrals, second quantization operator, Malliavin calculus and their relations with the Wick product and Wick renormalization are also briefly presented. A useful tool for Wick product is the S-transform which is also described without the introduction of generalized random variables.
文摘In this short note, we show that it is more natural to look the fractional Brownian motion as functionals of the standard white noises, and the fractional white noise calculus developed by Hu and Фksendal follows directly from the classical white noise functional calculus. As examples we prove that the fractional Girsanov formula, the Ito type integrals and the fractional Black-Scholes formula are easy consequences of their classical counterparts. An extension to the fractional Brownian sheet is also briefly discussed.
文摘Fundamental properties of Wick product of generalized operators are investigated. The annihilation and creation algebras are characterized from various points of view. Wick ordering widely used in quantum physics is interpreted as the Wick product of generalized operators.
