Related papers: Can time-homogeneous diffusions produce any distri…
A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the…
Recently Johansson and Rahman obtained the limiting multi-time distribution for the discrete polynuclear growth model, which is equivalent to a discrete TASEP model with step initial condition. In this paper, we obtain a finite time…
We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for observables of compact group extensions of nonuniformly…
We derive the continuous canonical distribution only by requiring the extensivity of the mean energy and the multiplicative probabilistic composition rule. The derivation is independent of the thermodynamic limit and moreover it does not…
We develop in this note a homogenization method to tackle the problem of a diffusion process through a cracked medium. We show that the cracked surface of the domain induces a source term in the homogenized equation. We assume that the…
In this paper a concentration inequality is proved for the deviation in the ergodic theorem in the case of discrete time observations of diffusion processes. The proof is based on the geometric ergodicity property for diffusion processes.…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
When the unconditioned process is a diffusion process $X(t)$ of drift $\mu(x)$ and of diffusion coefficient $D=1/2$, the local time $A(t)= \int_{0}^{t} d\tau \delta(X(\tau)) $ at the origin $x=0$ is one of the most important time-additive…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
Reflecting diffusions on continuum percolation clusters are considered. Assuming that the occupied region has a unique unbounded cluster and the cluster satisfies geometrical conditions such as volume regularity, isoperimetric conditions,…
In this paper, we consider nonnegative solutions of spatially heterogeneous Fisher-KPP type reaction-diffusion equations in the whole space. Under some assumptions on the initial conditions, including in particular the case of compactly…
We discuss a class of diffusion-type partial differential equations on a bounded interval and discuss the possibility of replacing the boundary conditions by certain linear conditions on the moments of order 0 (the total mass) and of…
In this paper, we study the asymptotic estimate of solution for a mixed-order time-fractional diffusion equation in a bounded domain subject to the homogeneous Dirichlet boundary condition. Firstly, the unique existence and regularity…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
We derive explicit solutions for time-fractional anomalous diffusion equations with diffusivity coefficients that depend on both space and time variables. These solutions are expressed in Fox-H and generalized Wright functions, which are…
Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of…
For an arbitrary diffusion process $X$ with time-homogeneous drift and variance parameters $\mu(x)$ and $\sigma^2(x)$, let $V_\varepsilon$ be $1/\varepsilon$ times the total time $X(t)$ spends in the strip…
The relation between relaxation and diffusion is investigated in a Hamiltonian system of globally coupled rotators. Diffusion is anomalous if and only if the system is going towards equilibrium. The anomaly in diffusion is not anomalous…
In the recent years, the notion of mixability has been developed with applications to optimal transportation, quantitative finance and operations research. An $n$-tuple of distributions is said to be jointly mixable if there exist $n$…
We study a symmetric diffusion $X$ on $\mathbb{R}^d$ in divergence form in a stationary and ergodic environment, with measurable unbounded and degenerate coefficients. We prove a quenched local central limit theorem for $X$, under some…