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Full-Text Articles in Other Mathematics
White Noise Based Stochastic Calculus Associated With A Class Of Gaussian Processes, Daniel Alpay, Haim Attia, David Levanony
White Noise Based Stochastic Calculus Associated With A Class Of Gaussian Processes, Daniel Alpay, Haim Attia, David Levanony
Mathematics, Physics, and Computer Science Faculty Articles and Research
Using the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus mainly on continuous functions with values in the Kondratiev space of stochastic distributions, where use is made of the topology of nuclear spaces. We also prove an associated Ito formula.
An Interpolation Problem For Functions With Values In A Commutative Ring, Daniel Alpay, Haim Attia
An Interpolation Problem For Functions With Values In A Commutative Ring, Daniel Alpay, Haim Attia
Mathematics, Physics, and Computer Science Faculty Articles and Research
It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we study an interpolation problem in this setting. A key tool is the principle of permanence of algebraic identities.
New Topological C-Algebras With Applications In Linear Systems Theory, Daniel Alpay, Guy Salomon
New Topological C-Algebras With Applications In Linear Systems Theory, Daniel Alpay, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
Motivated by the Schwartz space of tempered distributions S′ and the Kondratiev space of stochastic distributions S−1 we define a wide family of nuclear spaces which are increasing unions of (duals of) Hilbert spaces H′p,p∈N, with decreasing norms |⋅|p. The elements of these spaces are functions on a free commutative monoid. We characterize those rings in this family which satisfy an inequality of the form |f∗g|p≤A(p−q)|f|q|g|p for all p≥q+d, where * denotes the convolution in the monoid, A(p−q) is a strictly positive number and d is a fixed natural number (in this case we obtain commutative topological C-algebras). Such an …