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The Finite State Projection Approach for the Solution of the Master Equation and Its Applications to Stochastic Gene Regulatory Networks

出版	University of California, Santa Barbara, 2008
ISBN	05497028659780549702863
URL	http://books.google.com.hk/books?id=eOKkswEACAAJ&hl=&source=gbs_api

註釋This dissertation discusses the Finite State Projection (FSP) method for the direct computational analysis of probability distributions arising from discrete state Markov Processes. While the methods contained herein apply to a wide range of scientific inquiries, this study focuses on the treatment of chemically reacting biological systems. The probability distributions of such systems evolve according to a set of linear ordinary differential equations known as the chemical master equation (CME) or forward Kolmogorov equation. If the CME describes a system that has a finite number of distinct configurations, then the FSP method provides an exact analytical expression for its solution. When an infinite or extremely large number of variations is possible, the state space is truncated, and the FSP method provides a certificate of accuracy for how closely the FSP approximation matches the true solution. The proposed FSP algorithm systematically increases the projection space to meet any pre-specified error tolerance in the probability distribution. For any system in which a sufficiently accurate FSP solution exists, the FSP algorithm is shown to converge in a finite number of steps. The FSP approach is enhanced by taking advantage of well-known tools from modern control and dynamical systems theory such as minimal realizations, balanced truncation, linear perturbation theory, and coarse gridding approaches. Each such reduction has successfully improved the efficiency and applicability of the FSP, and more are envisioned to be possible.