相关论文: Integration by Parts and the KPZ Two-Point Functio…
We consider stochastic differential systems driven by a Brownian motion and a Poisson point measure where the intensity measure of jumps depends on the solution. This behavior is natural for several physical models (such as Boltzmann…
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…
The stationary reflected Brownian motion in a three-quarter plane has been rarely analyzed in the probabilistic literature, in comparison with the quarter plane analogue model. In this context, our main result is to prove that the…
We prove the existence of a unique Malliavin differentiable strong solution to a stochastic differential equation on the plane with merely integrable coefficients driven by the fractional Brownian sheet with Hurst parameters less than 1/2.…
A strong quasi-invariance principle and a finite-dimensional integration by parts formula as in the Bismut approach to Malliavin calculus are obtained through a suitable application of Lie's symmetry theory to autonomous stochastic…
We provide a probabilistic description of the stationary measures for the open KPZ on the spatial interval $[0,1]$ in terms of a Markov process $Y$, which is a Doob's $h$ transform of the Brownian motion killed at an exponential rate. Our…
We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coefficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic…
We present a field theoretic approach to capture the motion of a particle with dry friction for one- and two-dimensional diffusive particles, and further expand the framework for two-dimensional active Brownian particles. Starting with the…
The stochastic rotational invariance of an integration by parts formula inspired by the Bismut approach to Malliavin calculus is proved in the framework of the Lie symmetry theory of stochastic differential equations. The non-trivial effect…
We present a predictive local field theory for the nonequilibrium dynamics of interacting active Brownian particles with a spherical shape in two spatial dimensions. The theory is derived by a rigorous coarse-graining starting from the…
The Malliavin integration-by-parts formula is a key ingredient to develop stochastic analysis on the Wiener space. In this article we show that a suitable integration-by-parts formula also characterizes a wide class of Gaussian processes,…
Determinantal and permanental processes are point processes with a correlation function given by a determinant or a permanent. Their atoms exhibit mutual attraction of repulsion, thus these processes are very far from the uncorrelated…
We prove the existence of solutions to a non-linear, non-local, degenerate equation which was previously derived as the formal hydrodynamic limit of an active Brownian particle system, where the particles are endowed with a position and an…
We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially-dependent diffusion coefficient of the form $D(x)\sim |x|^c$, at constant temperature. The particle's probability distribution function…
This paper is a step in the direction of understanding the behavior of non-intersecting Brownian motions on the real line, when the number of particles becomes large. Consider 2k non-intersecting Brownian motions, all starting at the…
In this paper, we study the estimation of drift and diffusion coefficients in a two dimensional system of N interacting particles modeled by a degenerate stochastic differential equation. We consider both complete and partial observation…
We derive a quantum master equation from first principles to describe friction in one dimensional, collisional Brownian motion. We are the first to avoid an ill-defined square of the Dirac delta function by using localized wave packets…
Brownian motion of free particles on curved surfaces is studied by means of the Langevin equation written in Riemann normal coordinates. In the diffusive regime we find the same physical behavior as the one described by the diffusion…
We investigate piecewise-linear stochastic models as with regards to the probability distribution of functionals of the stochastic processes, a question which occurs frequently in large deviation theory. The functionals that we are looking…
We describe a two-dimensional model for active particles whose self-propulsion speed is not fixed, but varies in time, and whose motion is subject to both translational and rotational diffusion. In the conventional treatment of active…