We study a class of stochastic differential equation with linear fractal noise. By an auxiliary stochastic differential equation, we prove the existence and uniqueness of the solution under some mild assumptions. We a...We study a class of stochastic differential equation with linear fractal noise. By an auxiliary stochastic differential equation, we prove the existence and uniqueness of the solution under some mild assumptions. We also give some estimates of moments of the solution. The exponential stability of the solution is discussed.展开更多
In this paper,we investigate the numerical performance of a family of P-stable two-step Maruyama schemes in mean-square sense for stochastic differential equations with time delay proposed in[8,10]for a certain class ...In this paper,we investigate the numerical performance of a family of P-stable two-step Maruyama schemes in mean-square sense for stochastic differential equations with time delay proposed in[8,10]for a certain class of nonlinear stochastic delay differential equations with multiplicative white noises.We also test the convergence of one of the schemes for a time-delayed Burgers’equation with an additive white noise.Numerical results show that this family of two-step Maruyama methods exhibit similar stability for nonlinear equations as that for linear equations.展开更多
We study the adjunction property of the Jacquet–Emerton functor in certain neighborhoods of critical points in the eigencurve.As an application,we construct two-variable p-adic L-functions around critical points via ...We study the adjunction property of the Jacquet–Emerton functor in certain neighborhoods of critical points in the eigencurve.As an application,we construct two-variable p-adic L-functions around critical points via Emerton’s representation theoretic approach.展开更多
基金Acknowledgements This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11271294, 11171122）.
文摘We study a class of stochastic differential equation with linear fractal noise. By an auxiliary stochastic differential equation, we prove the existence and uniqueness of the solution under some mild assumptions. We also give some estimates of moments of the solution. The exponential stability of the solution is discussed.
基金This work was supported by the NSF of China(No.10901036)and AIRFORCE MURI.The authors thank the referees for their helpful suggestions for improving the paper.The first author also would like to thank Professor George Em Karniadakis for his hospitality when she was visiting Division of Applied Mathematics at Brown University.
文摘In this paper,we investigate the numerical performance of a family of P-stable two-step Maruyama schemes in mean-square sense for stochastic differential equations with time delay proposed in[8,10]for a certain class of nonlinear stochastic delay differential equations with multiplicative white noises.We also test the convergence of one of the schemes for a time-delayed Burgers’equation with an additive white noise.Numerical results show that this family of two-step Maruyama methods exhibit similar stability for nonlinear equations as that for linear equations.
文摘We study the adjunction property of the Jacquet–Emerton functor in certain neighborhoods of critical points in the eigencurve.As an application,we construct two-variable p-adic L-functions around critical points via Emerton’s representation theoretic approach.
