In this paper we shall give a simple and easy method to estimate the characteristic exponents for a class of second order linear different equation with periodic coefficient which frequently occurs in application.
In this paper, a second order linear differential equation is considered, and an accurate estimate method of characteristic exponent for it is presented. Finally, we give some examples to verify the feasibility of our...In this paper, a second order linear differential equation is considered, and an accurate estimate method of characteristic exponent for it is presented. Finally, we give some examples to verify the feasibility of our result.展开更多
We propose new numerical schemes for decoupled forward-backward stochastic differ- ential equations （FBSDEs） with jumps, where the stochastic dynamics are driven by a d- dimensional Brownian motion and an independen...We propose new numerical schemes for decoupled forward-backward stochastic differ- ential equations （FBSDEs） with jumps, where the stochastic dynamics are driven by a d- dimensional Brownian motion and an independent compensated Poisson random measure. A semi-discrete scheme is developed for discrete time approximation, which is constituted by a classic scheme for the forward SDE [20, 28] and a novel scheme for the backward SDE. Under some reasonable regularity conditions, we prove that the semi-discrete scheme can achieve second-order convergence in approximating the FBSDEs of interest; and such convergence rate does not require jump-adapted temporal discretization. Next, to add in spatial discretization, a fully discrete scheme is developed by designing accurate quadrature rules for estimating the involved conditional mathematical expectations. Several numerical examples are given to illustrate the effectiveness and the high accuracy of the proposed schemes.展开更多
基金Supported by Research Foundation of the Fujian Education Bureau (JA04158)the Natural Science Foundation of Fujian Province (No.2006J0209)the Foundation of Developing Science and Technology of Fuzhou University under the grant (2005-XQ-20).
文摘In this paper we shall give a simple and easy method to estimate the characteristic exponents for a class of second order linear different equation with periodic coefficient which frequently occurs in application.
基金supported by Foundation of Fujian Education Committee (JA08012)
文摘In this paper, a second order linear differential equation is considered, and an accurate estimate method of characteristic exponent for it is presented. Finally, we give some examples to verify the feasibility of our result.
基金The authors would like to thank the referees for their valuable comments, which improved much of the quality of the paper. This work is partially support- ed by the National Natural Science Foundations of China under grant numbers 91130003,11171189 and 11571206 by Natural Science Foundation of Shandong Province under grant number ZR2011AZ002+1 种基金 by the U.S. Department of Energy, Office of Science, Office of Ad- vanced Scientific Computing Research, Applied Mathematics program under contract number ERKJE45 and by the Laboratory Directed Research and Development program at the Oak Ridge National Laboratory, which is operated by UT-Battelle, LLC, for the U.S. Department of Energy under Contract DE-AC05-00OR22725.
文摘We propose new numerical schemes for decoupled forward-backward stochastic differ- ential equations （FBSDEs） with jumps, where the stochastic dynamics are driven by a d- dimensional Brownian motion and an independent compensated Poisson random measure. A semi-discrete scheme is developed for discrete time approximation, which is constituted by a classic scheme for the forward SDE [20, 28] and a novel scheme for the backward SDE. Under some reasonable regularity conditions, we prove that the semi-discrete scheme can achieve second-order convergence in approximating the FBSDEs of interest; and such convergence rate does not require jump-adapted temporal discretization. Next, to add in spatial discretization, a fully discrete scheme is developed by designing accurate quadrature rules for estimating the involved conditional mathematical expectations. Several numerical examples are given to illustrate the effectiveness and the high accuracy of the proposed schemes.
