Related papers: Whittaker functions and related stochastic process…
This paper investigates the relationship between the geometric properties of a domain and the diffusion dynamics of Brownian motion, with a specific focus on the phenomenon of "trapping" in terms of the behavior of stochastic processes.
The monograph is devoted to the study of stochastic area functionals of Brownian motions and of the associated heat kernels on Lie groups and Riemannian manifolds. It is essentially self-contained and as such can serve as a textbook on the…
A stochastic calculus is given for processes described by stochastic integrals with respect to fractional Brownian motions and Rosenblatt processes somewhat analogous to the stochastic calculus for It\^{o} processes. These processes for…
A stochastic sewing lemma which is applicable for processes taking values in Banach spaces is introduced. Applications to additive functionals of fractional Brownian motion of distributional type are discussed.
We obtain results on both weak and almost sure asymptotic behaviour of power variations of a linear combination of independent Wiener process and fractional Brownian motion. These results are used to construct strongly consistent parameter…
In this paper, we introduce two new matrix stochastic processes: fractional Wishart processes and $\varepsilon$-fractional Wishart processes with integer indices which are based on the fractional Brownian motions and then extend…
During training, weight matrices in machine learning architectures are updated using stochastic gradient descent or variations thereof. In this contribution we employ concepts of random matrix theory to analyse the resulting stochastic…
The paper deals with exponential functionals of the linear Brownian motion which arise in different contexts such as continuous time finance models and one-dimensional disordered models. We study some properties of these exponential…
Stochastic processes are considered on free loop spaces, geometric loop and diffeomorphism groups of real and complex manifolds. They are used for investigations of Wiener differentiable quasi-invariant measures on such groups relative to…
Brownian motions, martingales, and Wiener processes are introduced and studied for set valued functions taking values in the subfamily of compact convex subsets of arbitrary Banach space $X$. The present paper is an application of one the…
The quantum analog of the joint probability distributions describing a classical stochastic process is introduced. A prescription is given for constructing the quantum distribution associated with a sequence of measurements. For the case of…
Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level, are derived. This selective…
Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained. The results apply to general Gaussian processes including fractional Brownian motion, sub-fractional Brownian motion and…
We study interacting systems of linear Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. Our main objective has been to study the long range behavior of the…
We generalize the notion of the submartingale property and Doob's inequality. Furthermore, we show how the latter leads to new inequalities for several stochastic processes: certain time series, Levy processes, random walks, processes with…
Field-theoretic construction of functional representations of solutions of stochastic differential equations and master equations is reviewed. A generic expression for the generating function of Green functions of stochastic systems is put…
We consider a mixed stochastic differential equation driven by possibly dependent fractional Brownian motion and Brownian motion. Under mild regularity assumptions on the coefficients, it is proved that the equation has a unique solution.
Investigating the dynamics of learning in machine learning algorithms is of paramount importance for understanding how and why an approach may be successful. The tools of physics and statistics provide a robust setting for such…
This paper is concerned with the connection between G-Brownian Motion and analytic functions. We introduce the complex version of sublinear expectation, and then do the stochastic analysis in this framework. Furthermore, the conformal…
The area related to M. Liv\v{s}ic's characteristic matrix functions is too vast to be discussed in one paper and we selected for this article the problems which are close to our scientific interests. We discuss M.Liv\v{s}ic's results…