Related papers: Generalized Fock space and moments
Interacting systems of particles with generalized statistics are considered on both classical and quantum level. It is shown that all possible quantum states and corresponding processes can be represented in terms of certain specific…
This article is devoted to the stochastic anticipating equations with the extended stochastic integral with respect to the Gaussian processes of a special type. In the particular cases the solutions of such an equations are the well-known…
In this paper, we consider stochastic Schroedinger equations with two-dimensional white noise. Such equations are used to describe the evolution of an open quantum system undergoing a process of continuous measurement. Representations are…
Reversal of the time direction in stochastic systems driven by white noise has been central throughout the development of stochastic realization theory, filtering and smoothing. Similar ideas were developed in connection with certain…
Researchers from different areas have independently defined extensions of the usual weak convergence of laws of stochastic processes with the goal of adequately accounting for the flow of information. Natural approaches are convergence of…
We construct Euclidean random fields $X$ over $\R^d$, by convoluting generalized white noise $F$ with some integral kernels $G$, as $X=G* F$. We study properties of Schwinger (or moment) functions of $X$. In particular, we give a general…
Power law generalized covariance functions provide a simple model for describing the local behavior of an isotropic random field. This work seeks to extend this class of covariance functions to spatial-temporal processes for which the…
We consider a Poisson process $\eta$ on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of $\eta$. As a consequence we…
This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…
We construct a generalized dynamics for particles moving in a symmetric space-time, i.e. a space-time admitting one or more Killing vectors. The generalization implies that the effective mass of particles becomes dynamical. We apply this…
The article is devoted to the expansions of iterated Ito stochastic integrals based on generalized multiple Fourier series converging in the sense of norm in the space $L_2([t, T]^k),$ $k\in\mathbb{N}.$ The method of generalized multiple…
In $\R^d$, for any dimension $d\geq 1$, expansions of self-intersection local times of fractional Brownian motions with arbitrary Hurst coefficients in $(0,1)$ are presented. The expansions are in terms of Wick powers of white noises…
In this work we are concerned with the study of the strong order of convergence in the averaging principle for slow-fast systems of stochastic evolution equations in Hilbert spaces with additive noise. In particular the stochastic…
We consider a method for the approximation of iterated stochastic integrals of arbitrary multiplicity $k$ $(k\in \mathbb{N})$ with respect to the infinite-dimensional $Q$-Wiener process using the mean-square approximation method of iterated…
The paper is devoted to construction and investigation of some riggings of the $L^2$-space of Poisson white noise. A particular attention is paid to the existence of a continuous version of a function from a test space, and to the property…
Suppose we observe a trajectory of length $n$ from an exponentially $\alpha$-mixing stochastic process over a finite but potentially large state space. We consider the problem of estimating the probability mass placed by the stationary…
By introducing the small noise expansion techniques, we show that the fully nonlinear (non-Markovian) stochastic inflationary system, may be re-cast in terms of an infinite set of Wiener processes (stochastic equations with white noises).…
The goal of this paper is to show that fundamental concepts in higher-order Fourier analysis can be nauturally extended to the non-commutative setting. We generalize Gowers norms to arbitrary compact non-commutative groups. On the…
Stochastic integration with respect to Gaussian processes, such as fractional Brownian motion (fBm) or multifractional Brownian motion (mBm), has raised strong interest in recent years, motivated in particular by applications in finance,…
Consider a generalized time-dependent P\'olya urn process defined as follows. Let $d\in \mathbb{N}$ be the number of urns/colors. At each time $n$, we distribute $\sigma_n$ balls randomly to the $d$ urns, proportionally to $f$, where $f$ is…