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Path integral methods for stochastic differential equations.

Chow CC, Buice MA - J Math Neurosci (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Mathematical Biology Section, Laboratory of Biological Modeling, NIDDK, NIH, Bethesda, MD 20892 USA.

ABSTRACT
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.

No MeSH data available.


Vertices and propagators for Feynman diagrams in the Fitzhugh–Nagumo model. (a) Propagators  (solid–solid),  (solid–dashed),  (dashed–solid),  (dashed–dashed), (b) vertex , (c) vertex , (d) vertex
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Fig6: Vertices and propagators for Feynman diagrams in the Fitzhugh–Nagumo model. (a) Propagators (solid–solid), (solid–dashed), (dashed–solid), (dashed–dashed), (b) vertex , (c) vertex , (d) vertex

Mentions: The Feynman diagrams for the four propagators (39)–(42) and the two vertices in the action (38) are shown in Fig. 6. Fig. 6


Path integral methods for stochastic differential equations.

Chow CC, Buice MA - J Math Neurosci (2015)

Vertices and propagators for Feynman diagrams in the Fitzhugh–Nagumo model. (a) Propagators  (solid–solid),  (solid–dashed),  (dashed–solid),  (dashed–dashed), (b) vertex , (c) vertex , (d) vertex
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4385267&req=5

Fig6: Vertices and propagators for Feynman diagrams in the Fitzhugh–Nagumo model. (a) Propagators (solid–solid), (solid–dashed), (dashed–solid), (dashed–dashed), (b) vertex , (c) vertex , (d) vertex
Mentions: The Feynman diagrams for the four propagators (39)–(42) and the two vertices in the action (38) are shown in Fig. 6. Fig. 6

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Mathematical Biology Section, Laboratory of Biological Modeling, NIDDK, NIH, Bethesda, MD 20892 USA.

ABSTRACT
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.

No MeSH data available.