Second-order differential equations with random perturbations and small parameters

作者：Kamenskii M^*; Pergamenchtchikov S; Quincampoix M

来源：Proceedings of the Royal Society of Edinburgh: Section A Mathematics , 2017, 147(4): 763-779.

DOI：10.1017/S0308210516000354

• boundary-value problems
• stochastic averaging method
• Green functions

We consider boundary-value problems for differential equations of second order containing a Brownian motion (random perturbation) and a small parameter and prove a special existence and uniqueness theorem for random solutions. We study the asymptotic behaviour of these solutions as the small parameter goes to zero and show the stochastic averaging theorem for such equations. We find the explicit limits for the solutions as the small parameter goes to zero.

• 出版日期2017-8