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Blowup noise suppression and the impact on the dynamic behavior

Author: LiMi
Tutor: LiXiaoYue
School: Northeast Normal University
Course: Applied Mathematics
Keywords: Brownian motion It (?) Formula Stochastic Differential Equations Asymptotic behavior Blasting
CLC: O211.63
Type: Master's thesis
Year: 2011
Downloads: 9
Quote: 0
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Abstract


This paper studies nonlinear systems with random perturbations dx (t) = axm (t) dt bxn (t) dB (t) (1.1.1) where a, b ??gt; 0, t ≥ 0, m gt; 0, n ≥ 1, the initial value x (t0) gt; 0, B (t) is a standard Brownian motion for ordinary differential equation x (t) = axm (t), apparently when m gt; 1 , the equation in limited period of time will explode . purpose of this article is through such an ODE impose appropriate disturbance after disturbance to study some properties of stochastic differential equations . article constituted by the four chapters of the first chapter outlines the problems resulting from historical background, the main work and prove the main theorem in this article tools used in the second chapter , the first use of a single Lyapunov function of the system is random disturbance existence and uniqueness of solutions , which is the basis for later studies ; thus , give an understanding of a range of asymptotic behavior of the system in a single disturbance on the basis of random disturbance in the third chapter, further illustrates a dual system of some random disturbance dynamics of the fourth chapter of the summary of this article .

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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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