arXiv subjects

Thu Dang Thien Nguyen

Publications and source records attributed to Thu Dang Thien Nguyen.

3 recordsLinked to original sources

arXiv2018

Sticky Brownian motions and a probabilistic solution to a two-point boundary value problem

In this paper, we study a two-point boundary value problem consisting of the heat equation on the open interval $(0,1)$ with boundary conditions which relate first and second spatial derivatives at the boundary points. Moreover, the unique solution to this problem can be represented probabilistically in terms of a sticky Brownian motion. This probabilistic representation is attained from the stochastic differential equation for a sticky Brownian motion on the bounded interval $[0,1]$.

math.PR↗

arXiv2018

Particle model for the reservoirs in the simple symmetric exclusion process

In this paper, we will study the long time behavior of the simple symmetric exclusion process in the ``channel'' $Λ_N=[1,N]\cap \mathbb{N}$ with reservoirs at the boundaries. These reservoirs are also systems of particles which can be exchanged with the particles in the channel. The size $M$ of each reservoir is much larger than the one of the channel, i.e. $M=N^{1+α}$ for a fixed number $α>0$. Based on the size of the channel and the holding time at each reservoir, we will investigate some types of rescaling time.

math.PR↗

arXiv2018

Fick law and sticky Brownian motions

We consider an interacting particle system in the interval $[1,N]$ with reservoirs at the boundaries. While the dynamics in the channel is the simple symmetric exclusion process, the reservoirs are also particle systems which interact with the given system by exchanging particles. In this paper we study the case where the size of each reservoir is the same as the size of the channel . We will prove that the hydrodynamic limit equation is the heat equation with boundary conditions which relate first and second spatial derivatives at the boundaries for which we will prove the existence and uniqueness of weak solutions. The propagation of chaos property can also be derived.

math.PR↗