Related papers: Fractional Brownian motion with mean-density inter…
In this thesis, we develop analytical methods to study out-of-equilibrium stochastic processes driven by colored noise, i.e., noise with temporal correlations. These non-Markovian processes pose significant analytical challenges compared to…
Diffusive transport in many complex systems features a crossover between anomalous diffusion at short times and normal diffusion at long times. This behavior can be mathematically modeled by cutting off (tempering) beyond a mesoscopic…
This short note is motivated by a recently discovered connection between a drift-diffusion process in $n$-dimensional Euclidean space with a divergence-free drift sampled from a stationary and isotropic Gaussian ensemble of critical scaling…
One century after Einstein's work, Brownian Motion still remains both a fundamental open issue and a continous source of inspiration for many areas of natural sciences. We first present a discussion about stochastic and deterministic…
In this paper, we prove a mimicking theorem for stochastic processes with an additive Gaussian noise along with some entropy and transport type estimates. As an application of these results, we prove sharp quantitative propagation of chaos…
When a physical system evolves in a thermal bath at a constant temperature, it arrives eventually to an equilibrium state whose properties are independent of the kinetic parameters and of the precise evolution scenario. This is generically…
We propose a generalization of the widely used fractional Brownian motion (FBM), memory-multi-FBM (MMFBM), to describe viscoelastic or persistent anomalous diffusion with time-dependent memory exponent $\alpha(t)$ in a changing environment.…
Brownian motion is the erratic motion of an object due to collisions with the fluid in which it is immersed. In this work, we detail a tabletop laboratory demonstration of underdamped Brownian motion wherein a macroscopic particle resting…
We consider n-point sticky Brownian motions: a family of n diffusions that evolve as independent Brownian motions when they are apart, and interact locally so that the set of coincidence times has positive Lebesgue measure with positive…
In this work, we study the dynamics of a single active Brownian particle, as well as the collective behavior of interacting active Brownian particles, in a fluctuating heterogeneous environment. We employ a variant of the diffusing…
The dynamical behavior for a quantum Brownian particle is investigated under a random potential of the fractional iterative map on a one-dimensional lattice. For our case, the quantum expectation values can be obtained numerically from the…
Brownian motion is the only random process which is Gaussian, stationary and Markovian. Dropping the Markovian property, i.e. allowing for memory, one obtains a class of processes called fractional Brownian motion, indexed by the Hurst…
In this paper the solutions $u_{\nu}=u_{\nu}(x,t)$ to fractional diffusion equations of order $0<\nu \leq 2$ are analyzed and interpreted as densities of the composition of various types of stochastic processes. For the fractional equations…
Fractional Brownian motion (fBm) is a ubiquitous diffusion process in which the memory effects of the stochastic transport result in the mean squared particle displacement following a power law, $\langle {\Delta r}^2 \rangle \sim…
Brownian motion is a central scientific paradigm. Recently, due to increasing efforts and interests towards miniaturization and small-scale physics or biology, the effects of confinement on such a motion have become a key topic of…
We focus on the dynamics of a Brownian particle whose mass fluctuates. First we show that the behaviour is similar to that of a Brownian particle moving in a fluctuating medium, as studied by Beck [Phys. Rev. Lett. 87 (2001) 180601]. By…
We present Fractional Diffusion Bridge Models (FDBM), a novel generative diffusion bridge framework driven by an approximation of the rich and non-Markovian fractional Brownian motion (fBM). Real stochastic processes exhibit a degree of…
Spatiotemporal disorder has been recently associated to the occurrence of anomalous nonergodic diffusion of molecular components in biological systems, but the underlying microscopic mechanism is still unclear. We introduce a model in which…
This article introduces a novel construction of the two-dimensional fractional Brownian motion (2D fBm) with dependent components. Unlike similar models discussed in the literature, our approach uniquely accommodates the full range of model…
The generalized fractional Brownian motion is a Gaussian self-similar process whose increments are not necessarily stationary. It appears in applications as the scaling limit of a shot noise process with a power law shape function and…