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In certain applications, for instance biomechanics, turbulence, finance, or Internet traffic, it seems suitable to model the data by a generalization of a fractional Brownian motion for which the Hurst parameter $H$ is depending on the…
We provide a rigorous derivation of the brownian motion as the limit of a deterministic system of hard-spheres as the number of particles $N$ goes to infinity and their diameter $\varepsilon$ simultaneously goes to $0$, in the fast…
We consider additive functionals of systems of random measures whose initial configuration is given by a Poisson point process, and whose individual components evolve according to arbitrary Markovian or non-Markovian measure valued…
We prove functional limits theorems for the occupation time process of a system of particles moving independently in $R^d$ according to a symmetric $\alpha$-stable L\'evy process, and starting off from an inhomogeneous Poisson point measure…
We synthesize colloidal particles with various anisotropic shapes and track their orientationally resolved Brownian trajectories using confocal microscopy. An analysis of appropriate short-time correlation functions provides direct access…
We define a time dependent empirical process based on $n$ i.i.d.~fractional Brownian motions and establish Gaussian couplings and strong approximations to it by Gaussian processes. They lead to functional laws of the iterated logarithm for…
We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of a comprehensive market data enables us to identify all…
We find an explicit expression for the cross-covariance between stochastic integral processes with respect to a $d$-dimensional fractional Brownian motion (fBm) $B_t$ with Hurst parameter $H>1/2$, where the integrands are vector fields…
The analytical expressions for the time-dependent cross-correlations of the translational and rotational Brownian displacements of a particle with arbitrary shape are derived. The reference center is arbitrary, and the reference frame is…
By means of white noise analysis, we prove some limit theorems for nonlinear functionals of a given Volterra process. In particular, our results apply to fractional Brownian motion (fBm) and should be compared with the classical convergence…
We study fluctuation fields of orthogonal polynomials in the context of particle systems with duality. We thereby obtain a systematic orthogonal decomposition of the fluctuation fields of local functions, where the order of every term can…
We present a study of transport of a Brownian particle moving in periodic symmetric potential in the presence of asymmetric unbiased fluctuations. The particle is considered to move in a medium with periodic space dependent friction. By…
Passive scalar motion in a family of random Gaussian velocity fields with long-range correlations is shown to converge to persistent fractional Brownian motions in long times.
We have considered the underdamped motion of a Brownian particle in the presence of a correlated external random force. The force is modeled by an Ornstein-Uhlenbeck process. We investigate the fluctuations of the work done by the external…
We show that the past and future of half-plane Brownian motion at certain cutpoints are independent of each other after a conformal transformation. Like in Ito's excursion theory, the pieces between cutpoints form a Poisson process with…
Consider a finite system of Brownian particles on the real line. Each particle has drift and diffusion coefficients depending on its current rank relative to other particles, as in Karatzas, Pal and Shkolnikov (2012). We prove some…
We establish an invariance principle connecting boundary random walks on $\mathbb N$ with Feller's Brownian motions on $[0,\infty)$. A Feller's Brownian motion is a Feller process on $[0,\infty)$ whose excursions away from the boundary $0$…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…
We show in detail some results, outlined in a previous paper regarding the case of Brownian motion (BM), about the distribution of the $n$th-passage time of a one-dimensional diffusion obtained by a space or time transformation of BM,…
This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed…