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Equivalent Markov processes under gauge group.

M Caruso1, C Jarne2

  • 1Departamento de Física Teórica y del Cosmos, Universidad de Granada, Campus de Fuentenueva, Granada (18071), Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 15, 2015
PubMed
Summary
This summary is machine-generated.

All continuous-time Markov processes on denumerable state spaces are interconnected through gauge transformations. This study demonstrates this connection and its application in solving complex equations, including time-dependent cases.

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Area of Science:

  • * Mathematical Physics
  • * Stochastic Processes
  • * Quantum Field Theory

Background:

  • * Markov processes are fundamental in modeling systems with memoryless transitions.
  • * Previous work established connections between Markov processes and gauge transformations for specific cases, including time-dependent sample spaces.
  • * Resolving complex equations often requires advanced mathematical techniques.

Purpose of the Study:

  • * To demonstrate the general connection between Markov processes and gauge transformations.
  • * To present a unified framework for understanding these processes.
  • * To illustrate the application of gauge transformations in solving Markov process equations.

Main Methods:

  • * Analysis of Markov processes on denumerable state spaces with continuous time.
  • * Application of gauge (local) transformations to link different Markov processes.
  • * State space dilation and modification of probability distributions.

Main Results:

  • * All studied Markov processes are shown to be connected via gauge transformations.
  • * A general solution is found through state space dilation, with gauge transformations restoring the original process.
  • * The methodology is applicable to time-dependent sample spaces.

Conclusions:

  • * Gauge transformations provide a unifying principle for Markov processes.
  • * This framework offers a novel approach to solving equations involving stochastic processes.
  • * The results have implications for various fields utilizing Markovian modeling.