Derivation of the Chapman–Kolmogorov Equation and the Master Equation

Günter Haag
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Günter Haag: University of Stuttgart, Institute of Theoretical Physics II

Chapter Chapter 3 in Modelling with the Master Equation, 2017, pp 39-61 from Springer

Abstract: Abstract This chapter is important for the general understanding of the fundamental aspects of the Master equation. After the introduction of some concepts of probability theory, the Markov assumption is introduced and the Chapman–Kolmogorov equation for conditional probabilities derived. The Chapman–Kolmogorov equation provides the starting point for the derivation of the Master equation by considering the short-time evolution of the distribution in configuration space. The ensuing derivation of general properties of the Master equation helps to understand the broad field of possible applications. The derivation of equations of motion for mean values and variances on both, the stochastic and the quasi-deterministic level using the method of shift operators completes this chapter.

Date: 2017
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DOI: 10.1007/978-3-319-60300-1_3

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