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Path Integral Methods for Stochastic Differential Equations

Stochastic differential equations (SDEs) have multiple applications in mathematical neuroscience and are notoriously difficult. Here, we give a self-contained pedagogical review of perturbative field theoretic and path integral methods to calculate moments of the probability density function of SDEs...

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Detalles Bibliográficos
Autores principales: Chow, Carson C., Buice, Michael A.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2015
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4385267/
https://www.ncbi.nlm.nih.gov/pubmed/25852983
http://dx.doi.org/10.1186/s13408-015-0018-5
Descripción
Sumario:Stochastic differential equations (SDEs) have multiple applications in mathematical neuroscience and are notoriously difficult. Here, we give a self-contained pedagogical review of perturbative field theoretic and path integral methods to calculate moments of the probability density function of SDEs. The methods can be extended to high dimensional systems such as networks of coupled neurons and even deterministic systems with quenched disorder.