| In this paper,we mainly study the well-posedness and large deviation principle for a class of stochastic integro-differential equations.We established the existence and uniqueness of strong solutions and Freidlin-Wentzell type large deviation principle of s-tochastic integro-differential equations,which coefficients satisfying the standard linear growth and monotonicity conditions.We proved the existence and uniqueness of so-lutions based on the Euler’s approximation method.Concerning the Freidlin-Wentzell type large deviation principle for stochastic integro-differential equations driven by s-mall random noise,it can be obtained by using the contraction principle in the additive noise case;for the multiplicative noise case,based on the equivalence between the large deviation principle and the Laplace principle,we used the weak convergence approach to establish the corresponding Laplace principle.The content of the thesis is divided into five parts as follows:In Chapter 1,we introduce the research background and recent development of stochastic integro-differential equations and large deviations,and the main results of our paper is also briefly introduced.In Chapter 2,we mainly introduce some preliminaries for stochastic integro-differential equations and large deviation principle.In Chapter 3,we prove the uniqueness and existence of strong solutions for a class of stochastic integro-differential equations.In Chapter 4,we prove the large deviation principle for the additive noise case.In Chapter 5,we prove the large deviation principle for the multiplicative noise case. |
