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The Study on the Properties of Solutions for Two Classes of Stochastic Differential Equations

Author: JiaXiaoQing
Tutor: WangKe
School: Harbin Institute of Technology
Course: Computational Mathematics
Keywords: Stochastic Differential Equations Markov switch Lotka-Volterra model L_p estimate
CLC: O211.63
Type: Master's thesis
Year: 2010
Downloads: 42
Quote: 0
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Abstract


Stochastic differential equation as an important class of mathematical model, widely used in automatic control, biology, chemical reaction engineering , medicine, economics, demography , and many other fields of science . In order to better application of stochastic differential equations and a variety of specific equations for a lot of work , but also achieved great results , making it better able to play a role in many areas . But there are many problems the study is not clear enough , not deep enough, there are many areas worthy of our future generations to study and explore further . In the 1940s , Lotka and Volterra laid the theoretical basis of interspecific competition , and their interspecific competition equation have a significant impact on the development of modern ecological theory . Lotka-Volterra model of been in the deepening , it really is a very important for human understanding of biological populations , and to improve the biological environment has played an irreplaceable role model . With the rapid development of agriculture and industry , a large number of environmental issues , population extinction problem gradually Lotka - Volterra model will play a more important role . In this paper, a class of stochastic differential equations to understand the estimated Lotka-Volterra model with infinite delay switch with Markov random to do in-depth research , do some more in-depth promotion . In addition, we have a class of stochastic differential equations L_p estimated , making a better basis for future studies of the nature of this type of solution . The first chapter introduces the Lotka-Volterra model of research as well as the source of the problem , and we need to study some specific issues summarized . The second chapter describes some of the basic theory of the papers related to stochastic differential equations , and some have proved the theorem . Lotka-Volterra model of Chapter III , we prove that infinite delay switch with Markov random positive global solution existence and uniqueness the random final sector , there are some other nature of the solution . Chapter IV of our understanding of a class of stochastic differential equations L_p estimated .

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Theory of probability ( probability theory, probability theory ) > Random process > Stochastic differential equation
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