Related papers: Polarity of points for Gaussian random fields
In this paper, we obtain upper and lower bounds for the moments of the solution to a class of fractional stochastic heat equations on the ball driven by a Gaussian noise which is white in time, and with a spatial correlation in space of…
We generalize the generalized-squeezing problem to include fractional values of the squeezing order $n$. This approach allows us to determine the locations of critical points at which qualitative changes in behaviour occur and accurately…
We consider fluctuations in the distribution of critical points - saddle points, minima and maxima - of random gaussian fields. We calculate the asymptotic limits of the two point correlation function for various critical point densities,…
Covariant stochastic partial differential equations are studied in any dimension. A special class of such equations is selected and it is proven that the solutions can be analytically continued to Minkowski space-time yielding tempered…
We study the two-dimensional equations of motion for a charged particle subjected to white, thermal, and active noises in uniform a magnetic field. By deriving the corresponding Fokker Planck equation, analytical solutions for the joint…
We discuss the space-time determinantal random field which arises for the PNG model in one dimension and resembles the one for Dyson's Brownian motion. The information of interest for growth processes is carried by the edge statistics of…
We determine the exact Hausdorff measure functions for the range and level sets of a class of Gaussian random fields satisfying sectorial local nondeterminism and other assumptions. We also establish a Chung-type law of the iterated…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
In this article we prove large deviations principles for high minima of Gaussian processes with nonnegatively correlated increments on arbitrary intervals. Furthermore, we prove large deviations principles for the increments of such…
In this paper we consider a system of non-linear stochastic heat equations on $\mathbb{R}^d$ driven by a Gaussian noise which is white in time and has a homogeneous spatial covariance. Under some suitable regularity and non degeneracy…
We consider one-dimensional stochastic differential equations with a boundary condition, driven by a Poisson process. We study existence and uniqueness of solutions and the absolute continuity of the law of the solution. In the case when…
We consider a shot-noise field defined on a stationary determinantal point process on $\mathbb{R}^d$ associated with i.i.d. amplitudes and a bounded response function, for which we investigate the scaling limits as the intensity of the…
The paper presents bounds for the distributions of suprema for a particular class of sub-Gaussian type random fields defined over spaces with anisotropic metrics. The results are applied to random fields related to stochastic heat equations…
We consider stochastic heat equations with fractional Laplacian on $\mathbb{R}^d$. Here, the driving noise is generalized Gaussian which is white in time but spatially homogenous and the spatial covariance is given by the Riesz kernels. We…
A survey measuring quasar polarization vectors has been started in two regions towards the North and South Galactic Poles. Here, We review the discovery of significant correlations of orientations of polarization vectors over huge angular…
In this paper, we study central and non-central limit theorems for partial sum of functionals of general stationary Gaussian fields. We apply our result to study drift parameter estimation problems for some stochastic differential equations…
We consider the stochastic heat equation on $\mathbb R^d$ with multiplicative space-time white noise noise smoothed in space. For $d\geq 3$ and small noise intensity, the solution is known to converge to a strictly positive random variable…
Gaussian random fields on Euclidean spaces whose variances reach their maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximum of theirs trajectories have been evaluated using…
We consider the class of non-linear stochastic partial differential equations studied in \cite{conusdalang}. Equivalent formulations using integration with respect to a cylindrical Brownian motion and also the Skorohod integral are…
We establish the existence and uniqueness of strong solutions, in both the PDE and probabilistic sense, for a broad class of nonlinear stochastic partial differential equations (SPDEs) on a bounded domain $\mathscr{O}\subset \mathbb{R}^d$…