相关论文: Dynamical properties and characterization of gradi…

We construct a class of one-dimensional diffusion processes on the particles of branching Brownian motion that are symmetric with respect to the limits of random martingale measures. These measures are associated with the extended extremal…

We introduce a model of self-propelled particles carrying out a Brownian motion with a diffusion coefficient which depends on the local density of particles within a certain finite radius. Numerical simulations show that in a range of…

Let us consider a solution of the time-inhomogeneous stochastic differential equation driven by a Brownian motion with drift coefficient $b(t,x)=\rho\,{\rm sgn}(x)|x|^\alpha/t^\beta$. This process can be viewed as a distorted Brownian…

The Brownian motion of a particle in a one-dimensional periodic potential subjected to a uniform external force F is studied. Using the formula for the diffusion coefficient D obtained by other authors and an alternative one derived from…

In this work, we introduce a new method to prove the existence and uniqueness of a variational solution to the stochastic nonlinear diffusion equation $dX(t)={\rm div} [\frac{\nabla X(t)}{|\nabla X(t)|}]dt+X(t)dW(t) in…

We investigate the transience/recurrence of a non-Markovian, one-dimensional diffusion process which consists of a Brownian motion with a non-anticipating drift that has two phases---a transient to $+\infty$ mode which is activated when the…

We outline a reduction scheme for a class of Brownian dynamics which leads to meaningful corrections to the Smoluchowski equation in the overdamped regime. The mobility coefficient of the reduced dynamics is obtained by exploiting the…

In many physical or biological systems, diffusion can be described by Brownian motions with stochastic diffusion coefficients (DCs). In the present study, we investigate properties of the diffusion with a broad class of stochastic DCs with…

The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of…

Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. We analyse in detail this…

The movement of a particle described by Brownian motion is quantified by a single parameter, $D$, the diffusion constant. The estimation of $D$ from a discrete sequence of noisy observations is a fundamental problem in biological single…

This paper provides a new characterization of the stochastic invariance of a closed subset of R^d with respect to a diffusion. We extend the well-known inward pointing Stratonovich drift condition to the case where the diffusion matrix can…

We will consider the following stochastic differential equation (SDE): \begin{equation} X_t=X_0+\int_0^tb(X_s,\theta_0)ds+\sigma B_t,~~~t\in(0,T], \end{equation} where $\{B_t\}_{t\ge 0}$ is a fractional Brownian motion with Hurst index…

The Ludwig-Soret effect, the migration of a species due to a temperature gradient, has been extensively studied without a complete picture of its cause emerging. Here we investigate the dynamics of DNA and spherical particles sub jected to…

In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…

A rapidly increasing number of systems is identified in which the stochastic motion of tracer particles follows the Brownian law $\langle\mathbf{r}^2(t) \rangle\simeq Dt$ yet the distribution of particle displacements is strongly…

We consider a particular class of n-dimensional homogeneous diffusions all of which have an identity diffusion matrix and a drift function that is piecewise constant and scale invariant. Abstract stochastic calculus immediately gives us…

Complex spatial and temporal structures are inherent characteristics of turbulent fluid flows and comprehending them poses a major challenge. This comprehesion necessitates an understanding of the space of turbulent fluid flow…

We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time--reversal…

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…