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Asymptotic Properties of Solutions of Neutral Stochastic Functional Differential Equations

Author: HuRong
Tutor: HuShiGeng
School: Huazhong University of Science and Technology
Course: Probability Theory and Mathematical Statistics
Keywords: Neutral Equations Stochastic functional differential equations Stochastic delay differential equations Infinite Delay Asymptotic properties Semimartingale convergence theorem Markov modulated Moment stability Moment boundedness
CLC: O211.63
Type: PhD thesis
Year: 2009
Downloads: 120
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Abstract


Has a long history of research on the theory of stochastic differential equations, and so far has been a great deal of useful results. Needs in the field of chemical engineering and aviation theory, promoted the theory of neutral stochastic functional differential equations. Article discusses several types Neutral Stochastic Functional Differential Equations asymptotic properties. discuss a class of neutral stochastic differential equation with variable more delay, such equations contain ordinary neutral stochastic delay differential equations with a certain universality. application of the special Lyapunov function such variable delay the Neutral moment stability of stochastic differential equations discrimination law, such discrimination method for verifying the moment stability of the equations to be relatively easy at the same time, we will be a class of The specific function of ψ replace the common exponential function is introduced into the discussion, and the ψ function equation multiplied as a whole to consider a more general conclusions of the moment stability. then through random analysis of knowledge as well as Moment Inequalities, Burkholder-Davis-Gundy inequality and the Borel-Cantelli lemma skills, append the appropriate conditions, directly from the the moment stability launch track stability. Existence of solutions of the equation as a whole is to consider the asymptotic properties of the equations a prerequisite, linear growth condition is the easiest conditions guarantee overall solution of the equation. general lack of linear growth conditions, the local existence and uniqueness of solutions can only come from the local Lipschitz condition, which unable to support any discussion of the asymptotic properties. therefore, seek outside the linear growth condition overall Existence conditions of fundamental importance for Neutral Stochastic Functional Differential, special treatment in the project, we local Lipschitz condition, by appending the appropriate conditions, has been the existence of solutions of the equation overall the same time, under similar conditions, we also get a moment of Global Solutions sector and the average time moment bounded asymptotic properties conclusions. Moreover, we are also given the conclusions of the overall solution under specific growth conditions of existence and asymptotic properties. Finally, consider a neutral stochastic functional differential equations of the special form - Neutral stochastic delay differential equations, delay differential equations of a special form to obtain some of the easier applications conclusion. stochastic functional differential equations for a limited delay, the maximum delay T characterizes the system memory limits, however, in examine the reality of the development of the system, the actual identification of the above T is a problem. eliminate this difficulty a thorough method is simply the time delay T increases to infinity, so every point t (- ∞, t) This makes it necessary to discuss the Neutral infinite delay stochastic differential equations as a memory range., so it become a research topic of this paper we also introduced the ψ function neutral stochastic systems with infinite delay, get more ordinary Moments estimates and track estimated, the ψ function monotonically decreasing and monotonically increasing both cases, given the equations of moment stability and moment of orbital stability of the sector, as well as the equations and orbital bounded. Finally, we Markov Neutral Stochastic Functional Differential modulation were to take full account of the special nature of the Markov modulation system, under the premise of local Lipschitz conditions are met equally by appending the appropriate conditions, has been the existence of solutions of the equation overall, while under similar conditions, the conclusions of the asymptotic properties of the overall solution. Moreover, we have also given the existence of the whole solution in specific growth conditions and asymptotic properties of the corresponding conclusions.

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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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