The Study On The Properties Of Solutions For Two Classes Of Stochastic Differential Equations

As an important class of mathematical models ,Stochastic Differential Equationswidely used in automatic control, biological, chemical reaction engineering, medicine,economics, demography, and many other scientific fields. For better the application, peo-ple have done a lot of work in the stochastic differential equations and various concreteequations, and have also achieved great results,so it Can better play its role in many areas.However, many of the problems is the lack of clarity and not deep enough, there are manyareas worthing being explored further to study.In the 20th century, 40s, Lotka and Volterra Laid a theoretical foundation in Inter-specific competition, interspecific competition equation made by them has a major impacton the development of modern ecology. People has been deepening into Lotka-VolterraModel,because it is indeed a very important biological species model to human under-standing, and plays an irreplaceable role on improving Biological environment. With therapid development of industry and agriculture, a large number of environmental problems,increasingly serious problem of population extinction, Lotka-Volterra model will play amore important role. Therefore, solution of a class of stochastic differential equationswas estimated in this article, and stochastic Lotka-Volterra model of infinite delay withMarkovian Switching was in-depth study and done more in-depth promotion.In addition, we also do L_p Estimate to a class of stochastic differential equations,then it can make that we may have a better basis to study the nature of the type of solutionin the future.The first chapter introduces Some of the Lotka-Volterra model as well as the sourceof the problem, and we need to study some specific problems in the general.The second chapter introduces the paper involved some of the stochastic differentialequation basic theory and some theorem proved.In the third chapter, we prove the Stochastic Lotka-Volterra Model of Infinite Delaywith Markovian Switching with the global existence and uniqueness, stochastic ultimateboundedness and some other properties of solution.Chapter of a class of stochastic differential equations we do know was estimated.