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Laplace transforms of the logarithmic functions and their applications

Pathan M. A., Daman O.A.

Demonstratio Mathematica

2013

Vol. 46, nr 3

533--542

This paper deals with theorems and formulas using the technique of Laplace and Steiltjes transforms expressed in terms of interesting alternative logarithmic and related integral representations. The advantage of the proposed technique is illustrated by logarithms of integrals of importance in certain physical and statistical problems.

On q-deformed quantum stochastic calculus

Sniady P.

Probability and Mathematical Statistics

2001

Vol. 21, Fasc. 1

231--251

In this paper we investigate a quantum stochastic calculus built of creation, annihilation and number of particles operators which fulfill some deformed com-mutation relations. Namely, we introduce a deformation of a number of particles operator which hassimple commutation relations with well-known q-deformed creation and annihilation operators. Since all operators considered in this theory are bounded, we do not dealwith some difficulties of a non-deformed theory of Hudson and Parthasarathy [8]. We define stochastic integrals and estimate them in the operator norm. We prove Itô’s formula as well.

Time dependent Malliavin calculus on manifolds and application to nonlinear filtering '

Schiltz J.

Probability and Mathematical Statistics

1998

Vol. 18, Fasc. 2

319--334

In this paper, we prove, using Malliavin calculus, that under a global Hörmander condition the law of a Riemannian manifold valued stochastic process, a solution of a stochastic differential equation with time dependent coefficients, admits a C∞-density with respect to the Riemannian volume element. This result is applied to a nonlinear filtering problem with time dependent coefficients on manifolds.