Related papers: Stochastic processes on geometric loop and diffeom…

Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the…

An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the…

In this work we first introduce quasi-infinitely divisible (QID) random measures and formulate spectral representations. Then, we introduce QID stochastic integrals and present integrability conditions and continuity properties. Further, we…

Many stochastic processes are defined on special geometrical objects like spheres and cones. We describe how tools from harmonic analysis, i.e. Fourier analysis on groups, can be used to investigate probability density functions (pdfs) on…

If an experimentalist observes a sequence of emitted quantum states via either projective or positive-operator-valued measurements, the outcomes form a time series. Individual time series are realizations of a stochastic process over the…

We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…

Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…

The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…

We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds with boundary in Hilbert spaces for stochastic partial differential equations driven by Wiener processes and Poisson random…

In the article, integration of temporal functions in (possibly non-UMD) Banach spaces with respect to (possibly non-Gaussian) fractional processes from a finite sum of Wiener chaoses is treated. The family of fractional processes that is…

In this paper analogically as quadratic stochastic operators and processes we define cubic stochastic operator (CSO) and cubic stochastic processes (CSP). These are defined on the set of all probability measures of a measurable space. The…

Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…

We study the properties of solutions of stochastic differential equations driven by processes generating loops in free nilpotent groups. We are in particular interested in existence and smoothness for the density.

We describe, in an intrinsic way and using the global chart provided by Ito's parallel transport, a generalisation of the notion of geodesic (as critical path of an energy functional) to diffusion processes on Riemannian manifolds. These…

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…

Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…

Stochastic processes are proposed whose master equations coincide with classical wave, telegraph, and Klein-Gordon equations. Similar to predecessors based on the Goldstein-Kac telegraph process, the model describes the motion of particles…

This primer explains how continuous-time stochastic processes (precisely, Brownian motion and other Ito diffusions) can be defined and studied on manifolds. No knowledge is assumed of either differential geometry or continuous-time…

The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite…

For many stochastic processes there is an underlying coordinate space, $V$, with the process moving from point to point in $V$ or on variables (such as spin configurations) defined with respect to $V$. There is a matrix of transition…