Suppressive Influence of Time- Space White Noise on the Explosion of Solutions of Stochastic Fokker- Planck Delay Differential Equations  

作　　者：Augustine O. Atonuje Jonathan Tsetimi 

机构地区：[1]Department of Mathematics and Computer Science, Delta State University, Abraka, Nigeria.

出　　处：《Journal of Mathematics and System Science》2016年第7期284-290,共7页数学和系统科学（英文版）

摘　　要：It is generally known that the solutions of deterministic and stochastic differential equations （SDEs） usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventually blow up or explode in finite time. If the drift and diffusion functions are globally Lipschitz, linear growth may still be experienced, as well as a possible blow-up of solutions in finite time. In this paper, a nonlinear scalar delay differential equation with a constant time lag is perturbed by a multiplicative Ito-type time - space white noise to form a stochastic Fokker-Planck delay differential equation. It is established that no explosion is possible in the presence of any intrinsically slow time - space white noise of Ito - type as manifested in the resulting stochastic Fokker- Planck delay differential equation. Time - space white noise has a role to play since the solution of the classical nonlinear equation without it still exhibits explosion.

关 键 词：Explosion non-linear stochastic Fokker Planck delay differential equation time - space white noise finite time. 

分 类 号：O211.63[理学—概率论与数理统计] TK123[理学—数学]