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Stochastic Models

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Book cover Reaction Kinetics: Exercises, Programs and Theorems

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Abstract

Having exhaustively studied deterministic models of reactions, the aim of the present chapter is to introduce and discuss the induced kinetic Markov process endowed with stochastic kinetics, also called the usual stochastic model of reactions. The two main differences compared to the previous models are that the state space is now discrete and the nature of determination is probabilistic. First we deal with the master equation, i.e., the evolution equation for the probability of the process being in a particular state. We formulate the analogue of “mass action type kinetics” and outline various characterizations of the underlying process which also serve as the basis for simulation methods. Then further evolution equations are discussed; in particular, the characterization of short- and long-term behavior of the induced kinetic Markov process and properties of the stationary states are covered. At the end of the chapter, we broadly discuss the relationship between the induced kinetic Markov process and the solution of the induced kinetic differential equation.

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Authors and Affiliations

  1. Department of Analysis, Budapest University of Technology and Economics, Budapest, Hungary

    János Tóth

  2. Chemical Kinetics Laboratory, Eötvös Loránd University, Budapest, Hungary

    János Tóth

  3. Department of Stochastics, Budapest University of Technology and Economics, Budapest, Hungary

    Attila László Nagy

  4. Department of Mathematics, North Carolina State University, Raleigh, USA

    Dávid Papp

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  1. János Tóth
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  2. Attila László Nagy
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  3. Dávid Papp
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Tóth, J., Nagy, A.L., Papp, D. (2018). Stochastic Models. In: Reaction Kinetics: Exercises, Programs and Theorems. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-8643-9_10

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