The pathwise convergence of a distributed, asynchronous stochastic approximation (SA) scheme is analyzed. The conditions imposed on the step size and noise are the weakest in comparison with the existing ones. The ste...The pathwise convergence of a distributed, asynchronous stochastic approximation (SA) scheme is analyzed. The conditions imposed on the step size and noise are the weakest in comparison with the existing ones. The step sizes in different processors are allowed to be different, and the time-delays between processors are also allowed to be different and even time-varying.展开更多
This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations （SDDEs） of ItS-type. The method is proved to be mean-square convergent of order min{1/2,p...This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations （SDDEs） of ItS-type. The method is proved to be mean-square convergent of order min{1/2,p} under the Lipschitz condition and the linear growth condition, where p is the exponent of HSlder condition of the initial function. Stability criteria for this type of method are derived. It is shown that for certain choices of the flexible parameter p the derived method can have a better stability property than more commonly used numerical methods. That is, for some p, the asymptotic MS-stability bound of the method will be much larger than that of the Euler-Maruyama method. Numerical results are reported confirming convergence properties and comparing stability properties of methods with different parameters p. Finally, the vectorised simulation is discussed and it is shown that this implementation is much more efficient.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 2666100 and 69804010) the National Key Project of China.
文摘The pathwise convergence of a distributed, asynchronous stochastic approximation (SA) scheme is analyzed. The conditions imposed on the step size and noise are the weakest in comparison with the existing ones. The step sizes in different processors are allowed to be different, and the time-delays between processors are also allowed to be different and even time-varying.
基金This work is supported by National Natural Science Foundation of China （Nos. 11401594, 11171125, 91130003） and the New Teachers＇ Specialized Research Fund for the Doctoral Program from Ministry of Education of China （No. 20120162120096）.
文摘This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations （SDDEs） of ItS-type. The method is proved to be mean-square convergent of order min{1/2,p} under the Lipschitz condition and the linear growth condition, where p is the exponent of HSlder condition of the initial function. Stability criteria for this type of method are derived. It is shown that for certain choices of the flexible parameter p the derived method can have a better stability property than more commonly used numerical methods. That is, for some p, the asymptotic MS-stability bound of the method will be much larger than that of the Euler-Maruyama method. Numerical results are reported confirming convergence properties and comparing stability properties of methods with different parameters p. Finally, the vectorised simulation is discussed and it is shown that this implementation is much more efficient.
