部分截断Euler-Maruyama数值方法的保正性

截断Euler-Maruyama(EM)方法是求解高度非线性随机微分方程的一种有效的方法。但是,在诸如生物种群和股票价格的模型中,随机微分方程的解为正时才有实际意义。因此,结合截断EM方法研究随机微分方程数值解的保正性具有实践性意义。通过对随机微分方程进行对数变换,在保证截断EM方法收敛的情况下,证明了随机微分方程的数值解和解析解的指数可积性,进而得到数值解能保持解析解正性的结果。

Positive preserving property of the partially truncated Euler-Maruyama method

Truncated Euler-Maruyama(EM)method is an effective one for solving highly nonlinear stochastic differential equations.However,in such models as biological populations and stock prices,it is of practical significance when the solution of stochastic differential equation is positive.Therefore,it is significant to study the positivity preserving property of numerical solutions of stochastic differential equations with truncated EM method.By logarithmic transformation of stochastic differential equation,the exponential integrability of numerical solution and analytical solution of stochastic differential equation is proved under the condition of ensuring the convergence of truncated EM method,and the result that numerical solution can keep the positive of analytical solution is obtained.