Related papers: Tangent Processes on Wiener Space
We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's…
Some parts of stochastic analysis on curved spaces are revisted. A concise proof of the quasi-invariance of the Wiener measure on the path spaces over a Riemannian manifold is presented. The shifts are allowed to be in the Cameron-Martin…
A rotation in a Euclidean space V is an orthogonal map on V which acts locally as a plane rotation with some fixed angle. We give a classification of all pairs of rotations in finite-dimensional Euclidean space, up to simultaneous…
We develop a theory of Brownian motion of a massive particle, including the effects of inertia (Kramers' problem), in spaces with curvature and torsion. This is done by invoking the recently discovered generalized equivalence principle,…
We consider the space of convex functions defined in the Euclidean $n$-dimensional space, which are lower semi-continuous and tend to infinity at infinity. We study real-valued valuations defined on this space of functions, which are…
The purpose of this article is to present the second type fundamental relationship between the generalized Fourier--Feynman transform and the generalized convolution product on Wiener space. The relationships in this article are also…
We study several important fine properties for the family of fractional Brownian motions with Hurst parameter $H$ under the $(p,r)$-capacity on classical Wiener space introduced by Malliavin. We regard fractional Brownian motions as Wiener…
We present the foundations of the theory of functions of bounded variation and sets of finite perimeter in abstract Wiener spaces.
The geodesic motion of pseudo-classical spinning particles in the Euclidean Taub-NUT space is analysed. The generalized Killing equations for spinning space are investigated and the constants of motion are derived in terms of the solutions…
The moving average of the complex modulus of the analytic wavelet transform provides a robust time-scale representation for signals to small time shifts and deformation. In this work, we derive the Wiener chaos expansion of this…
We provide a new and elementary proof of the continuity theorem for the wavelet and left-inverse wavelet transforms on the spaces $ \mathcal{S}_0(\mathbb{R}^n) $ and $ \mathcal{S}(\mathbb{H}^{n+1})$. We then introduce and study a new class…
We study multi-dimensional normal approximations on the Poisson space by means of Malliavin calculus, Stein's method and probabilistic interpolations. Our results yield new multi-dimensional central limit theorems for multiple integrals…
We introduce the notion of {\em covariance measure structure} for square integrable stochastic processes. We define Wiener integral, we develop a suitable formalism for stochastic calculus of variations and we make Gaussian assumptions only…
We consider randomized computation of continuous data in the sense of Computable Analysis. Our first contribution formally confirms that it is no loss of generality to take as sample space the Cantor space of infinite FAIR coin flips. This…
This paper sheds light on the essential characteristics of geodesics, which frequently occur in considerations from motion in Euclidean space. Focus is mainly on a method of obtaining them from the calculus of variations, and an explicit…
Wick rotation in area tensor Regge calculus is considered. The heuristical expectation is confirmed that the Lorentzian quantum measure on a spacelike area should coincide with the Euclidean measure at the same argument. The consequence is…
Described is n-level quantum system realized in the n-dimensional ''Hilbert'' space H with the scalar product G taken as a dynamical variable. The most general Lagrangian for the wave function and G is considered. Equations of motion and…
We study functions of bounded variation defined in an abstract Wiener space X, relating the variation of a function u on a convex open set O in X to the behavior near t=0 of T(t)u, T(t) being the Ornstein--Uhlenbeck semigroup in O.
The famous Hadwiger theorem classifies all rigid motion invariant continuous valuations on convex sets as linear conbinations of quermassintegrals. We prove much more general result. We classify continuous valuations which are invariant…
Let $M$ be the space of real $n\times m$ matrices which can be identified with the Euclidean space $R^{nm}$. We introduce continuous wavelet transforms on $M$ with a multivalued scaling parameter represented by a positive definite symmetric…