Although we do not intend to give a general, formal definition, the stochastic mean-field dynamics we present in these notes can be conceived as the random evolution of a system comprised by N interacting components which is: (a) invariant in law for permutation of the components; (b) such that the contribution of each component to the evolution of any other is of order 1 1 N . The permutation invariance clearly does not allow any freedom in the choice of the geometry of the interaction; however, this is exactly the feature that makes these models analytically treatable, and therefore attractive for a wide scientific community.

Stochastic Mean-Field Dynamics and Applications to Life Sciences

Dai Pra, Paolo
2019-01-01

Abstract

Although we do not intend to give a general, formal definition, the stochastic mean-field dynamics we present in these notes can be conceived as the random evolution of a system comprised by N interacting components which is: (a) invariant in law for permutation of the components; (b) such that the contribution of each component to the evolution of any other is of order 1 1 N . The permutation invariance clearly does not allow any freedom in the choice of the geometry of the interaction; however, this is exactly the feature that makes these models analytically treatable, and therefore attractive for a wide scientific community.
2019
978-3-030-15095-2
Mean-field stochastic dynamics, applications to life sciences
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1009644
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