Three-step master equation: class of parametric stationary solutions
H.C. Rosu, M.A. Reyes, F. Valencia
TL;DR
This paper derives a class of parametric stationary solutions for the three-step master equation using discrete Riccati equations, linking solutions to Markov processes with specific transition rate renormalizations.
Contribution
It introduces a novel approach to solving the three-step master equation by connecting it with discrete Riccati equations, providing parametric stationary solutions dependent on a free constant.
Findings
Stationary solutions depend on a negative parameter D
Solutions correspond to Markov processes with renormalized transition rates
The approach offers a new analytical method for solving complex master equations
Abstract
We examine the three-step master equation from the standpoint of the general solution of the associated discrete Riccati equation. We report by this means stationary master solutions depending on a free constant parameter, denoted by D, that should be negative in order to assure the positivity of the solution. These solutions correspond to different discrete Markov processes characterized by the value of D, which is related to specific renormalizations of the transition rates of the chain of states
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