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On the approximation theorem of Wong-Zakai type for the Lasota operator

Dawidowicz A. L., Twardowska K.

Opuscula Mathematica

2010

Vol. 30, no. 3

255-270

We consider in this paper a stochastic evolution equation with Professor A. Lasota's operator as the infinitesimal generator of a strongly continuous semigroup of transformations and with Hammerstein operator connected with a noise being the Wiener process. We show that such evolution equation satisfies the Wong-Zakai type approximation theorem. The idea of the definition of the Lasota operator has the origin in the mathematical model of the creation and differentiation of cells in biology and medicine.

A variational representation for positive functionals of infinite dimensional Brownian motion

Budhira A., Dupuis P.

Probability and Mathematical Statistics

2000

Vol. 20, Fasc. 1

39--61

A variational representation for positive functionals of a Hilbert space valued Wiener process (W(-)) is proved. This representation is then used to prove a large deviations principle for the family {Gε(W{‧))} ε>0 where G is an appropriate family of measurable maps from the Wiener space to some Polish space.