Estimate on the Pathwise Lyapunov Exponent of the Linear Stochastic Differential Equations with Constant Coefficients

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Yazdanbakhsh, Proshat | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 43582 (02)
University: Sharif University Of Technology
Department: Mathematical Sciences
Advisor(s): Zohuri Zangeneh, Bijan
Abstract:
The application of Stochastic Differential Equations in branches like nonlinear control,robatic systems, financial mathematics and etc. has grown impressively nowadays. In this thesis, we are going to introduce this equations and study their stability. First, we will present methods to check the stability of nonlinear systems dx(t) = f(x(t); t)dt using Lyapunov’s theorem.Then we will study stability of autonomous systems using it’s results. In the case of instability, we will study the possibility of stabilizing the stochastic equations dx(t) = Ax(t)dt + Σn i=1 Bix(t)dWi(t) by using Brownian motions and these methods. In the end, we will study the stabilizablity conditions of instable autonomous systems using controllable properties.
Keywords:
Stability ; Stabilization ; Controllability ; Lyapunov Exponent ; Stabilizable

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