相关论文: On Positive Recurrence of Constrained Diffusion Pr…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
We consider diffusion in arbitrary spatial dimension d with the addition of a resetting process wherein the diffusive particle stochastically resets to a fixed position at a constant rate $r$. We compute the non-equilibrium stationary state…
Divergence and vorticity damping, which operate upon horizontal divergence and relative vorticity, are explicit diffusion mechanisms used in dynamical cores to ensure stability. To avoid numerical blow-up from excessively strong diffusion,…
This paper deals with an inverse source problem for the $1$D time-fractional diffusion equation by using boundary measurement. The conditional stability in identification of the unknown source term is proved on the basis of the Fourier…
Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical…
Our aim is to study the backward problem, i.e. recover the initial data from the terminal observation, of the subdiffusion with time dependent coefficients. First of all, by using the smoothing property of solution operators and a…
We consider a diffusion process $X$ in a random potential $\V$ of the form $\V_x = \S_x -\delta x$ where $\delta$ is a positive drift and $\S$ is a strictly stable process of index $\alpha\in (1,2)$ with positive jumps. Then the diffusion…
We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be…
This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…
The well-posedness for SDEs with singularity in both space and distribution variables is derived, where the interacting drift term is bounded and Lipschitz continuous under total variation distance and the diffusion term is allowed to be…
This work introduces the extended Skorokhod problem (ESP) and associated extended Skorokhod map (ESM) that enable a pathwise construction of reflected diffusions that are not necessarily semimartingales. Roughly speaking, given the closure…
We construct diffusions with values in the nonnegative orthant, normal reflection along each of the axes, and two pairs of local drift/variance characteristics assigned according to rank; one of the variances is allowed to vanish, but not…
Irreversible drift-diffusion processes are very common in biochemical reactions. They have a non-equilibrium stationary state (invariant measure) which does not satisfy detailed balance. For the corresponding Fokker-Planck equation on a…
Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the…
This work focuses on stability of regime-switching diffusions consisting of continuous and discrete components, in which the discrete component switches in a countably infinite set and its switching rates at current time depend on the…
We consider a positive recurrent one-dimensional diffusion process with continuous coefficients and we establish stable central limit theorems for a certain type of additive functionals of this diffusion. In other words we find some…
We present and analyze a first order least squares method for convection dominated diffusion problems, which provides robust L2 a priori error estimate for the scalar variable even if the given data f in L2 space. The novel theoretical…
We investigate the obstacle problem for generalized Dean--Kawasaki equations driven by correlated conservative noise, establishing the existence, uniqueness, and $L^1$-stability of stochastic kinetic solutions. Our core strategy combines a…
We study a finite system of diffusions on the half-line, absorbed when they hit zero, with a correlation effect that is controlled by the proportion of the processes that have been absorbed. As the number of processes in the system becomes…
The classical result by It\^o on the existence of strong solutions of stochastic differential equations (SDEs) with Lipschitz coefficients can be extended to the case where the drift is only measurable and bounded. These generalizations are…