In this article, we study the rate of convergence of the polygonal approximation to multiple stochastic integral Sp （f） of fractional Brownian motion of Hurst parameter H 〈 1/2 when the fractional Brownian motion i...In this article, we study the rate of convergence of the polygonal approximation to multiple stochastic integral Sp （f） of fractional Brownian motion of Hurst parameter H 〈 1/2 when the fractional Brownian motion is replaced by its polygonal approximation. Under different conditions on f and for different p, we obtain different rates.展开更多
In this paper, we have investigated the problem of the convergence rate of the multiple integralwhere f ∈ Cn＋1（[0, T ]n） is a given function, π is a partition of the interval [0, T ] and {BtHi ,π} is a family of...In this paper, we have investigated the problem of the convergence rate of the multiple integralwhere f ∈ Cn＋1（[0, T ]n） is a given function, π is a partition of the interval [0, T ] and {BtHi ,π} is a family of interpolation approximation of fractional Brownian motion BtH with Hurst parameter H 1/2. The limit process is the multiple Stratonovich integral of the function f . In view of known results, the convergence rate is different for different multiplicity n. Under some mild conditions, we obtain that the uniform convergence rate is 2H in the mean square sense, where is the norm of the partition generating the approximations.展开更多
In this paper, we propose the multiple Stratonovich integral driven by G-Brownian motion under the G-expectation framework. Then based on G-Itöformula, we obtain the relationship between Hermite polynomials a...In this paper, we propose the multiple Stratonovich integral driven by G-Brownian motion under the G-expectation framework. Then based on G-Itöformula, we obtain the relationship between Hermite polynomials and multiple G-Stratonovich integrals by using mathematical induction method.展开更多
基金partially supported by NNSF of China (60534080)the firstauthor is supported in part by the National Science Foundation (DMS0504783)
文摘In this article, we study the rate of convergence of the polygonal approximation to multiple stochastic integral Sp （f） of fractional Brownian motion of Hurst parameter H 〈 1/2 when the fractional Brownian motion is replaced by its polygonal approximation. Under different conditions on f and for different p, we obtain different rates.
基金supported by the scientific research fund of Central South University for Nationalities (YZZ09005)
文摘In this paper, we have investigated the problem of the convergence rate of the multiple integralwhere f ∈ Cn＋1（[0, T ]n） is a given function, π is a partition of the interval [0, T ] and {BtHi ,π} is a family of interpolation approximation of fractional Brownian motion BtH with Hurst parameter H 1/2. The limit process is the multiple Stratonovich integral of the function f . In view of known results, the convergence rate is different for different multiplicity n. Under some mild conditions, we obtain that the uniform convergence rate is 2H in the mean square sense, where is the norm of the partition generating the approximations.
文摘In this paper, we propose the multiple Stratonovich integral driven by G-Brownian motion under the G-expectation framework. Then based on G-Itöformula, we obtain the relationship between Hermite polynomials and multiple G-Stratonovich integrals by using mathematical induction method.
