A theorem allowing the derivation of deterministic evolution equations from stochastic evolution equations. Tensorial, spinorial, and other extensions
G. Costanza
Departamento de Física, Universidad Nacional de San Luis, Chacabuco 917, 5700 San Luis, Argentina.
Recibido el 1 de junio de 2012. ]]> Aceptado el 16 de noviembre de 2012.
Abstract
The proof of a new extension of a theorem that allows to construct deterministic evolution equations from a set of discrete stochastic evolution equation is developed. The present extension allows to handle evolution equations of dynamical variables that are tensors of any rank. Due that the almost paradigmatic field that uses tensors is relativity, an illustrative example is given and the equations that allows to find the geodesics is derived from a set of discrete stochastic evolution equations. Extension to dynamical variables described by spinor indices or "arbitrary labels" are given.
Keywords: Evolution equations; stochastic processes.
Resumen
La demostración de una nueva extensión de un teorema, que permite la construcción de ecuaciones de evolución deterministas a partir de un conjunto de ecuaciones de evolución discretas estocásticas, es desarrollada. La extensión presente, permite manejar ecuaciones de evolución de variables dinámicas que son tensores de cualquier rango. Como el más paradigmático campo que usa tensores es la relatividad, un ejemplo ilustrativo es dado y las ecuaciones que permiten hallar las geodésicas es derivado de un conjunto de ecuaciones de evolución discretas estocásticas. Extensiones a variables dinámicas descriptas por índices espinoriales o "etiquetas arbitrarias" son dados.
Descriptores: Ecuaciones de evolución; procesos estocásticos.
]]> PACS: 05.45.Ra
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