Theoretical and numerical studies on stochastic dynamical systems확률 동역학계의 이론적, 수치적 연구

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We present general procedure of numerical scheme to solve stochastic differential equations by generation of stochastic trajectories. The generation of each sample trajectory is performed by discrete time approximation obtained from stochastic Taylor expansion. This method is readily applicable to dynamical systems driven by arbitrary type of noise, provided there exists a way to describe the accumulated random increment of the noise as a Markov process, and obtain its probability distribution. Using the systematic procedure, we obtain numerical schemes for two important non-Gaussian noises, the dichotomous Markov noise and the Poissonian white shot noise. Analytical expressions of the probability distributions for the random increment of the two different types of the noise are possible for each case. We further propose a simplified weak scheme by replacing the random increment with a simple random variable satisfying the same moment properties up to the required order. This scheme not only reduces the computation time significantly but also easy to develop, since it requires only lower order moments of the random increment of the noise rather than the whole distribution of it. The accuracies and efficiencies of the proposed algorithms are examined by applying the numerical schemes to prototypical model systems that possess analytical solutions. We study formal reduction scheme of a continuous Markov process with two metastable states to a discrete rate process and examine time dependent behavior of the rate in the presence of time dependent external forces or fluctuating barrier heights. Although the weak noise assumption has to be maintained for the rate description, no further assumption is required on the time scale of the external driving force. The derivation of the discrete rate equation is pursued in terms of two state-distributions and two site-localizing functions. These auxiliary functions are constructed as linear combinations of first two Floquet...
Advisors
Lee, Eok-Kyunresearcher이억균researcher
Description
한국과학기술원 : 화학과,
Publisher
한국과학기술원
Issue Date
2007
Identifier
268760/325007  / 020035820
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 화학과, 2007. 8, [ vi, 84 p. ]

Keywords

stochastic process; stochastic differential equation; Fokker-Planck equation; 확률과정; 확률미분방정식; 포커-플랑크 식; stochastic process; stochastic differential equation; Fokker-Planck equation; 확률과정; 확률미분방정식; 포커-플랑크 식

URI
http://hdl.handle.net/10203/31684
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=268760&flag=dissertation
Appears in Collection
CH-Theses_Ph.D.(박사논문)
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