Occurence Probabilities of Stochastic Paths
Dirk Helbing, Rolf Molini
TL;DR
This paper derives an analytical formula to calculate the occurrence probabilities of Markovian stochastic paths, aiding in the analysis of random walk trajectories and the numerical evaluation of the contracted path integral solution of the master equation.
Contribution
It introduces a new analytical formula for path occurrence probabilities in Markov processes, enhancing the analysis of stochastic trajectories and computational methods.
Findings
Provides an explicit formula for path probabilities
Facilitates efficient trajectory analysis in Markov models
Supports numerical evaluation of the contracted path integral
Abstract
An analytical formula for the occurence probability of Markovian stochastic paths with repeatedly visited and/or equal departure rates is derived. This formula is essential for an efficient investigation of the trajectories belonging to random walk models and for a numerical evaluation of the `contracted path integral solution' of the discrete master equation [Phys. Lett. A 195, 128 (1994)].
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