Related papers: Continuity of Local Time: An applied perspective
The operational meaning of spacetime fluctuations is discussed. Classical spacetime geometry can be viewed as encoding the relations between the motions of test particles in the geometry. By analogy, quantum fluctuations of spacetime…
In this paper we give necessary and sufficient conditions for a cylindrical continuous local martingale to be the stochastic integral with respect to a cylindrical Brownian motion. In particular we consider the class of cylindrical…
In this article we discuss the existence of local time for a class of Gaussian processes which appears as the solutions to some stochastic evolution equations. We show that on small intervals such processes are Gaussian integrators…
We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…
The purpose of this article is to review the developments related to the notion of local fractional derivative introduced in 1996. We consider its definition, properties, implications and possible applications. This involves the local…
The paper presents an investigation of local-time effect - one of the manifestations of macroscopic fluctuations phenomena. Was shown the existence of the named effect for longitudinal distance between locations of measurements up to 500…
We introduce a stochastic version of Gubinelli's sewing lemma, providing a sufficient condition for the convergence in moments of some random Riemann sums. Compared with the deterministic sewing lemma, adaptiveness is required and the…
Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by…
The main purpose of this work is to define planar self-intersection local time by an alternative approach which is based on an almost sure pathwise approximation of planar Brownian motion by simple, symmetric random walks. As a result,…
We consider a 1-dimensional Brownian motion whose diffusion coefficient varies when it crosses the origin. We study the long time behavior and we establish different regimes, depending on the variations of the diffusion coefficient:…
We provide sufficient conditions on the coefficients of a stochastic functional differential equation with bounded memory driven by Brownian motion which guarantee existence and uniqueness of a maximal local and global strong solution for…
Heat fluctuations are studied in a dissipative system with both mechanical and stochastic components for a simple model: a Brownian particle dragged through water by a moving potential. An extended stationary state fluctuation theorem is…
Our investigation is specially motivated by the stochastic version of a common model of potential spread in a dendritic tree. We do not assume the noise in the junction points to be Markovian. In fact, we allow for long-range dependence in…
In this article we introduce cylindrical fractional Brownian motions in Banach spaces and develop the related stochastic integration theory. Here a cylindrical fractional Brownian motion is understood in the classical framework of…
The relativistic generalization of a free Brownian motion theory is presented. The global characteristics of the relaxation are {\it explicitly} found for the velocity and momentum (stochastic) kinetics. It is shown that the thermal…
There is a solution to the problem of asymptotic completeness in many body scattering theory that offers a specific view of the quantum unitary dynamics which allows for the straightforward introduction of local time for every, at least…
The question how the extremal values of a stochastic process achieved on different time intervals are correlated to each other has been discussed within the last few years on examples of the running maximum of a Brownian motion, of a…
We study a system of reflected Brownian motions on the positive half-line in which each particle has a drift toward the origin determined by the local times at the origin of all the particles. If this local time drift is too strong, such…
Let $W$ be a one-dimensional Brownian motion starting from 0. Define $Y(t)= \int_0^t{\d s \over W(s)} := \lim_{\epsilon\to0} \int_0^t 1_{(|W(s)|> \epsilon)} {\d s \over W(s)} $ as Cauchy's principal value related to local time. We prove…
In this paper we investigate the class of grey Brownian motions $B_{\alpha,\beta}$ ($0<\alpha<2$, $0<\beta\leq1$). We show that grey Brownian motion admits different representations in terms of certain known processes, such as fractional…