Related papers: Talagrand Inequality on Free Path Space and Applic…

One of the key ingredients to successfully apply Stein's method for distributional approximation are solutions to the Stein equations and their derivatives. Using Barbour's generator approach, one can solve for the solutions to the Stein…

In this paper we study an asymptotic expansion for the distribution of a random motion of a particle driven by a Markov process in diffusion approximation. We show that the singularly perturbed equation of a Markovian random motion can be…

This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of…

We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the…

Splitting probabilities quantify the likelihood of a given outcome out of competitive events. This key observable of random walk theory, historically introduced as the gambler's ruin problem, is well understood for memoryless (Markovian)…

We propose threshold diffusion processes as unique solutions to stochastic differential equations with step-function coefficients, and obtain explicit expressions for the conditional Laplace transform of the hitting times and the potential…

We develop a probabilistic characterisation of trajectorial expansion rates in non-autonomous stochastic dynamical systems that can be defined over a finite time interval and used for the subsequent uncertainty quantification in Lagrangian…

Experimental data from a turbulent jet flow is analysed in terms of an additive, continuous stochastic process where the usual time variable is replaced by the scale. We show that the energy transfer through scales is well described by a…

The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…

A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…

The normalised partial sums of values of a nonnegative multiplicative function over divisors with appropriately restricted sizes of a random permutation from the symmetric group define trajectories of a stochastic process. We prove a…

Near equilibrium, thermodynamic intuition suggests that fast, irreversible processes will dissipate more energy and entropy than slow, quasistatic processes connecting the same initial and final states. Here, we test the hypothesis that…

Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…

The stochastic differential and integral equations describing the system of particles weakly interacting among themselves which are absorbed and scattered by particles of a medium are considered. The time-dependent transport equation with…

We consider a stochastic differential equation for a charged particle in a stochastic magnetic field, known as A-Langevin equation. The solution of the equation is found, and the Lagrange velocity correlation function is calculated in…

The computation of the probability of the first-passage time through a given threshold of a stochastic process is a classic problem that appears in many branches of physics. When the stochastic dynamics is markovian, the probability admits…

Systems with interacting degrees of freedom play a prominent role in stochastic thermodynamics. Our aim is to use the concept of detached path probabilities and detached entropy production for bipartite Markov processes and elaborate on a…

We derive an exact equation governing two-particle backwards mean-squared dispersion for both deterministic and stochastic tracer particles in turbulent flows. For the deterministic trajectories, we probe the consequences of our formula for…

We prove the free analogue of the transportation cost inequality for tracial distributions of non-commutative self-adjoint (also unitary) multi-variables based on random matrix approximation procedure.

One way to define the concentration of measure phenomenon is via Talagrand inequalities, also called transportation-information inequalities. That is, a comparison of the Wasserstein distance from the given measure to any other absolutely…