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2 - Dynamical Systems and Markov Processes

from Part I - Concepts from Modeling, Inference, and Computing

Published online by Cambridge University Press:  17 August 2023

Steve Pressé
Affiliation:
Arizona State University
Ioannis Sgouralis
Affiliation:
University of Tennessee, Knoxville
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Summary

In this chapter we present dynamical systems and their probabilistic description. We distinguish between system descriptions with discrete and continuous state-spaces as well as discrete and continuous time. We formulate examples of statistical models including Markov models, Markov jump processes, and stochastic differential equations. In doing so, we describe fundamental equations governing the evolution of the probability of dynamical systems. These equations include the master equation, Langevin equation, and Fokker–Plank equation. We also present sampling methods to simulate realizations of a stochastic dynamical process such as the Gillespie algorithm. We end with case studies relevant to chemistry and physics.

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Chapter
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Data Modeling for the Sciences
Applications, Basics, Computations
, pp. 40 - 107
Publisher: Cambridge University Press
Print publication year: 2023

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