In this paper,we investigate the strong Feller property of stochastic differential equations(SDEs)with super-linear drift and Hölder diffusion coefficients.By utilizing the Girsanov theorem,coupling method,trunca...In this paper,we investigate the strong Feller property of stochastic differential equations(SDEs)with super-linear drift and Hölder diffusion coefficients.By utilizing the Girsanov theorem,coupling method,truncation method and the Yamada-Watanabe approximation technique,we derived the strong Feller property of the solution.展开更多
In this paper,numerical methods for the time-changed stochastic differential equations of the form dY(t)=a(Y(t))dt+b(Y(t))dE(t)+s(Y(t))dB(E(t))are investigated,where all the coefficients a(·),b(·)and s(·...In this paper,numerical methods for the time-changed stochastic differential equations of the form dY(t)=a(Y(t))dt+b(Y(t))dE(t)+s(Y(t))dB(E(t))are investigated,where all the coefficients a(·),b(·)and s(·)are allowed to contain some super-linearly growing terms.An explicit method is proposed by using the idea of truncating terms that grow too fast.Strong convergence in the finite time of the proposed method is proved and the convergence rate is obtained.The proposed method is also proved to be able to reproduce the asymptotic stability of the underlying equation in the almost sure sense.Simulations are provided to demonstrate the theoretical results.展开更多
At first,by means of Kartsatos technique,we reduce the impulsive differential equation to a second order nonlinear impulsive homogeneous equation.We find some suitable impulse functions such that all the solutions to ...At first,by means of Kartsatos technique,we reduce the impulsive differential equation to a second order nonlinear impulsive homogeneous equation.We find some suitable impulse functions such that all the solutions to the equation are oscillatory.Several criteria on the oscillations of solutions are given.At last,we give an example to demonstrate our results.展开更多
基金Supported by the National Natural Science Foundation of China(11926322)the Fundamental Research Funds for the Central Universities of South-Central MinZu University(CZY22013,3212023sycxjj001)。
文摘In this paper,we investigate the strong Feller property of stochastic differential equations(SDEs)with super-linear drift and Hölder diffusion coefficients.By utilizing the Girsanov theorem,coupling method,truncation method and the Yamada-Watanabe approximation technique,we derived the strong Feller property of the solution.
基金Wei Liu would like to thank Shanghai Rising-Star Program(Grant No.22QA1406900)Science and Technology Innovation Plan of Shanghai(Grant No.20JC1414200)the National Natural Science Foundation of China(Grant Nos.11871343,11971316 and 12271368)for their financial support.
文摘In this paper,numerical methods for the time-changed stochastic differential equations of the form dY(t)=a(Y(t))dt+b(Y(t))dE(t)+s(Y(t))dB(E(t))are investigated,where all the coefficients a(·),b(·)and s(·)are allowed to contain some super-linearly growing terms.An explicit method is proposed by using the idea of truncating terms that grow too fast.Strong convergence in the finite time of the proposed method is proved and the convergence rate is obtained.The proposed method is also proved to be able to reproduce the asymptotic stability of the underlying equation in the almost sure sense.Simulations are provided to demonstrate the theoretical results.
基金supported by the National Natural Science Foundation of China (No.1097123131071560)+1 种基金the NSF of Guangdong Province (No.101510225010000048151027501000053)
文摘At first,by means of Kartsatos technique,we reduce the impulsive differential equation to a second order nonlinear impulsive homogeneous equation.We find some suitable impulse functions such that all the solutions to the equation are oscillatory.Several criteria on the oscillations of solutions are given.At last,we give an example to demonstrate our results.
