In this paper, we first study the existence and uniqueness of solutions to the stochastic differential equations driven by fractional Brownian motion with non-Lipschitz coefficients. Then we investigate the explosion ...In this paper, we first study the existence and uniqueness of solutions to the stochastic differential equations driven by fractional Brownian motion with non-Lipschitz coefficients. Then we investigate the explosion time in stochastic differential equations driven by fractional Browmian motion with respect to Hurst parameter more than half with small diffusion.展开更多
We prove that Euler＇s approximations for stochastic differential equations driven by infinite many Brownian motions and with non-Lipschitz coefficients converge almost surely. Moreover, the rate of convergence is obt...We prove that Euler＇s approximations for stochastic differential equations driven by infinite many Brownian motions and with non-Lipschitz coefficients converge almost surely. Moreover, the rate of convergence is obtained.展开更多
In this paper, we first prove Schilder＇s theorem in H？lder norm （0 ≤ α 〈1） with respect to Cr,p-capacity. Then, based on this result, we further prove a sharpening of large deviation principle for increments of...In this paper, we first prove Schilder＇s theorem in H？lder norm （0 ≤ α 〈1） with respect to Cr,p-capacity. Then, based on this result, we further prove a sharpening of large deviation principle for increments of fractional Brownian motion for Cr,p-capacity in the stronger topology.展开更多
基金Supported in part by National Natural Science Foundation of China (Grant Nos. 10901065,60934009)
文摘In this paper, we first study the existence and uniqueness of solutions to the stochastic differential equations driven by fractional Brownian motion with non-Lipschitz coefficients. Then we investigate the explosion time in stochastic differential equations driven by fractional Browmian motion with respect to Hurst parameter more than half with small diffusion.
基金Supported by National Natural Science Foundation of China (Grant Nos.10901065 and 11271013)Fundamental Research Funds for the Central Universities,Huazhong University of Science and Technology (Grant No.2012QN028)
文摘We prove that Euler＇s approximations for stochastic differential equations driven by infinite many Brownian motions and with non-Lipschitz coefficients converge almost surely. Moreover, the rate of convergence is obtained.
基金Supported by NSFC(Grant Nos.11271013,61273074,61201065,61203219,11471104)the Fundamental Research Funds for the Central Universities,HUST(Grant Nos.2012QN028 and 2014TS066)+2 种基金IRTSTHN(Grant No.14IRSTHN023)Ph D research startup foundation of He’nan Normal University(Grant No.5101019170120)Youth Science Foundation of He’nan Normal University(Grant No.5101019279032)
文摘In this paper, we first prove Schilder＇s theorem in H？lder norm （0 ≤ α 〈1） with respect to Cr,p-capacity. Then, based on this result, we further prove a sharpening of large deviation principle for increments of fractional Brownian motion for Cr,p-capacity in the stronger topology.
