A Segal-Langevin Type Stochastic Differential Equation on a Space Of Generalized Functionals

Kallianpur, Gopinath ; Mitoma, Itaru

Canadian journal of mathematics, Tome 44 (1992) no. 3, pp. 524-552

Résumé

Let E′ be the dual of a nuclear Fréchet space E and L*(t) the adjoint operator of a diffusion operator L(t) of infinitely many variables, which has a formal expression: A weak form of the stochastic differential equation dX(t) = dW(t) + L*(t)X(t)dtis introduced and the existence of a unique solution is established. The solution process is a random linear functional (in the sense of I. E. Segal) on a space of generalized functionals on E′. The above is an appropriate model for the central limit theorem for an interacting system of spatially extended neurons. Applications to the latter problem are discussed.

Détail

DOI : 10.4153/CJM-1992-034-8

Mots-clés : 46F25, 60F05, 60H15, 35K22, Weak solution, SDE, Fréchet derivative, generalized functional space, central limit theorem, system of neurons

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