C_h空间中无穷时滞随机泛函微分方程解的存在唯一性

Existence and uniqueness of solution to stochastic functional differential equations with infinite delay at phase space C_h

研究了一类具有无穷时滞的随机泛函微分方程,以空间(C_h,|·|_h)为相空间,利用Picard迭代法,借助于Bihari不等式,得到了系数在满足非Lipschitz条件和弱化的线性增长条件时解的存在唯一性.

This paper deals with the existence and uniqueness of the solution to stochastic functional differential equations with infinite delay.In the phase space C_h,under the non-Lipschitz condition and a weakened linear growth condition for the coefficients and by means of the Picard approximations and Bihari inequality,the existence-uniqueness theorem is obtained.