Related papers: Gaussian lower bound for the FIN diffusion

We consider a real-valued diffusion process with a linear jump term driven by a Poisson point process and we assume that the jump amplitudes have a centered density with finite moments. We show upper and lower estimates for the density of…

In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…

We derive, through subordination techniques, a generalized Feynman-Kac equation in the form of a time fractional Schrodinger equation. We relate such equation to a functional which we name the subordinated local time. We demonstrate through…

In this paper, we mainly introduce a general method to study the existence and uniqueness of solution of free boundary problems with partially degenerate diffusion.

The solution of time fractional partial differential equations in general exhibit a weak singularity near the initial time. In this article we propose a method for solving time fractional diffusion equation with nonlocal diffusion term. The…

Simple upper and lower bounds are obtained for the integral $\int_0^x\mathrm{e}^{-\gamma t}t^\nu I_\nu(t)\,\mathrm{d}t$, $x>0$, $\nu>-\frac{1}{2}$, $0<\gamma<1$. Most of our bounds for this integral are tight as $x\rightarrow\infty$. We…

Lower bounds for persistence probabilities of stationary Gaussian processes in discrete time are obtained under various conditions on the spectral measure of the process. Examples are given to show that the persistence probability can decay…

The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous-time random walks with exponential and heavy-tailed waiting time distributions. The space dependent variable-order…

We establish a quantitative lower bound on the reach of flat norm minimizers for boundaries in $\mathbb{R}^2$.

In the recent literature, the g-subdiffusion equation involving Caputo fractional derivatives with respect to another function has been studied in relation to anomalous diffusions with a continuous transition between different subdiffusive…

We show a lower estimate of the Milnor number of an isolated hypersurface singularity, via its Newton number. We also obtain analogous estimate of the Milnor number of an isolated singularity of a similar complete intersection variety.

We consider a diffusion in a Gaussian random environment that is white in time and study the large-scale behavior of the quenched density with respect to the Lebesgue measure. We show that under diffusive rescaling, the fluctuations of the…

We investigate the local times of a continuous-time Markov chain on an arbitrary discrete state space. For fixed finite range of the Markov chain, we derive an explicit formula for the joint density of all local times on the range, at any…

We give explictly the probability density of the local time of the Brox diffusion at first passage times. Such formula is used to find the moments and to related the minima and maxima of the environment to the most and least visted points…

We investigate the fractional diffusion limit of a Linear Boltzmann equation with heavy-tailed velocity equilibrium in a half-space with Maxwell boundary conditions. We derive a new confined version of the fractional Laplacian and show…

Linear singularly perturbed convection-diffusion problems with characteristic layers are considered in three dimensions. We demonstrate the sharpness of our recently obtained upper bounds for the associated Green's function and its…

The problem how to approximately determine the absolute value of the Fisher information measure for a general parametric probabilistic system is considered. Having available the first and second moment of the system output in a parametric…

Given a matrix $A \in \mathbb{R}^{m\times d}$ with singular values $\sigma_1\geq \cdots \geq \sigma_d$, and a random matrix $G \in \mathbb{R}^{m\times d}$ with iid $N(0,T)$ entries for some $T>0$, we derive new bounds on the Frobenius…

We propose a local modification of the standard subdiffusion model by introducing the initial Fickian diffusion, which results in a multiscale diffusion model. The developed model resolves the incompatibility between the nonlocal operators…

We prove sharp estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations on a bounded domain subject to a homogeneous Dirichlet boundary condition. Important special cases are the…