Equivalent Markov processes under gauge group

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-depende...

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Autores principales: Caruso, M., Jarne, C.
Formato: JOUR
Materias:
Continuous time systems
Markov processes
Continuous-time
Gauge group
Gauge transformation
General solutions
Initial problem
Sample space
Time dependent
Probability distributions
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_15393755_v92_n5_p_Caruso
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_15393755_v92_n5_p_Caruso2023-10-03T16:22:52Z Equivalent Markov processes under gauge group Caruso, M. Jarne, C. Continuous time systems Markov processes Continuous-time Gauge group Gauge transformation General solutions Initial problem Sample space Time dependent Probability distributions 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)PLEEE81539-375510.1103/PhysRevE.90.022125]. 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. © 2015 American Physical Society. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_15393755_v92_n5_p_Caruso
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Continuous time systems
Markov processes
Continuous-time
Gauge group
Gauge transformation
General solutions
Initial problem
Sample space
Time dependent
Probability distributions
spellingShingle Continuous time systems
Markov processes
Continuous-time
Gauge group
Gauge transformation
General solutions
Initial problem
Sample space
Time dependent
Probability distributions
Caruso, M.
Jarne, C.
Equivalent Markov processes under gauge group
topic_facet Continuous time systems
Markov processes
Continuous-time
Gauge group
Gauge transformation
General solutions
Initial problem
Sample space
Time dependent
Probability distributions
description 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)PLEEE81539-375510.1103/PhysRevE.90.022125]. 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. © 2015 American Physical Society.
format JOUR
author Caruso, M.
Jarne, C.
author_facet Caruso, M.
Jarne, C.
author_sort Caruso, M.
title Equivalent Markov processes under gauge group
title_short Equivalent Markov processes under gauge group
title_full Equivalent Markov processes under gauge group
title_fullStr Equivalent Markov processes under gauge group
title_full_unstemmed Equivalent Markov processes under gauge group
title_sort equivalent markov processes under gauge group
url http://hdl.handle.net/20.500.12110/paper_15393755_v92_n5_p_Caruso
work_keys_str_mv AT carusom equivalentmarkovprocessesundergaugegroup
AT jarnec equivalentmarkovprocessesundergaugegroup
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