title: Equivalent Markov processes under gauge group.
abstract: We have studied Markov processes on denumerable state space and continuous time. We found that all these processes are connected via gauge transformations. We have used this result before as a method to resolve equations, included the case in a previous work in which the sample space is time-dependent [Phys. Rev. E 90, 022125 (2014)]. We found a general solution through dilation of the state space, although the prior probability distribution of the states defined in this new space takes smaller values with respect to that in the initial problem. The gauge (local) group of dilations modifies the distribution on the dilated space to restore the original process. In this work, we show how the Markov process in general could be linked via gauge (local) transformations, and we present some illustrative examples for this result.
authors.affiliation: Departamento de Física Teórica y del Cosmos, Universidad de Granada, Campus de Fuentenueva, Granada (18071), Spain.
authors.forename: M
authors.initials: M
authors.lastname: Caruso
authors.affiliation: Instituto de Física de Buenos Aires - CONICET Facultad de Ciencias Exactas y Naturales. Pabellón I Ciudad Universitaria Post Code:1428. Buenos Aires - Argentina.
authors.forename: C
authors.initials: C
authors.lastname: Jarne