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Stochastic evolutions driven by non-linear white noise

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Accardi L. , Boukas A.

Probability and Mathematical Statistics

2002

tom Vol. 22, Fasc. 1

141--154

We prove the existence and uniqueness theorem for stochastic differential equations with bounded coefficients driven by the renormalized square of white noise.These equations are interpreted as sesquilinear forms on the linear span of the exponential vectors (of the first order white noise) and the existence theorem is establishedon the space of these forms.

Interpolated subspaces of exponential vectors of the unbounded operators in Banach spaces

100%

Dmytryshyn M. , Lopushansky O.

Demonstratio Mathematica

2004

tom Vol. 37, nr 1

149--158

It is shown that the spectral subspaces of the unbounded operators in Ba-nach spaces and also their integer degrees can be described with help of interpolation. The spectral subspaces of operators are described on the basis of abstract Bernstein inequality. The results are applied to research of the root subspaces of regular elliptic operators in a bounded domains.