Optimal lower bounds on hitting probabilities for stochastic heat equations in spatial dimension k >= 1

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Mathematical models involving multiple scales are essential for the description of physical systems. In particular, these models are important for the simulation of time-dependent phenomena, such as the heat flow, where the Laplacian contains mixed and ind ...

Motivation: The majority of genome analysis tools and pipelines require data to be decrypted for access. This potentially leaves sensitive genetic data exposed, either because the unencrypted data is not removed after analysis, or because the data leaves t ...

We present and analyze a novel wavelet-Fourier technique for the numerical treatment of multidimensional advection–diffusion–reaction equations based on the COmpRessed SolvING (CORSING) paradigm. Combining the Petrov–Galerkin technique with the compressed ...

We study vector-valued solutions u(t, x) is an element of R-d to systems of nonlinear stochastic heat equations with multiplicative noise, ...

Fractional Levy motion has been derived from its generalized Langevin equation via path integrals in earlier works and has since proven to be a useful model for nonlocal and non-Markovian processes, especially in the context of nondiffusive transport. Here ...

We investigate experimentally and theoretically diffusiophoretic separation of negatively charged particles in a rectangular channel flow, driven by CO2 dissolution from one side-wall. Since the negatively charged particles create an exclusion zone near th ...

We consider a system of d non-linear stochastic fractional heat equations in spatial dimension 1 driven by multiplicative d-dimensional space-time white noise. We establish a sharp Gaussian-type upper bound on the two-point probability density function of ...

We consider sample path properties of the solution to the stochastic heat equation, in Rd or bounded domains of Rd, driven by a Levy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solut ...

Wave phenomena manifest in nature as electromagnetic waves, acoustic waves, and gravitational waves among others. Their descriptions as partial differential equations in electromagnetics, acoustics, and fluid dynamics are ubiquitous in science and engineer ...

While in recent years gyrokinetic simulations have become the workhorse for theoretical turbulence and transport studies in the plasma core, their application to the edge and scrape-off layer (SOL) region presents significant challenges. In particular, ste ...

In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point argument. Unlike ...

Given a sequence L & x2d9;epsilon of Levy noises, we derive necessary and sufficient conditions in terms of their variances sigma 2(epsilon) such that the solution to the stochastic heat equation with noise sigma(epsilon)-1L & x2d9;epsilon converges in law ...

We present a multi-laboratory effort to describe the structural and dynamical properties of duplex B-DNA under physiological conditions. By processing a large amount of atomistic molecular dynamics simulations, we determine the sequence-dependent structura ...

We study the regularity of the probability density function of the supremum of the solution to the linear stochastic heat equation. Using a general criterion for the smoothness of densities for locally nondegenerate random variables, we establish the smoot ...

We study the Cauchy problem for the half Ginzburg- Landau-Kuramoto (hGLK) equation with the second order elliptic operator having rough coecients and potential type perturbation. The blow-up of solutions for hGLK equation with non-positive nonlinearity is ...

Optimal lower bounds on hitting probabilities for stochastic heat equations in spatial dimension k >= 1

Chat with Graph Search

Numerical methods for deterministic and stochastic differential equations with multiple scales and high contrasts

Crypt4GH: a file format standard enabling native access to encrypted data

Wavelet-Fourier CORSING techniques for multidimensional advection-diffusion-reaction equations

Polarity Of Almost All Points For Systems Of Nonlinear Stochastic Heat Equations In The Critical Dimension

Truncated Levy motion through path integrals and applications to nondiffusive suprathermal ion transport

CO2-Driven diffusiophoresis and water cleaning: similarity solutions for predicting the exclusion zone in a channel flow

Optimal lower bounds on hitting probabilities for non-linear systems of stochastic fractional heat equations

Path properties of the solution to the stochastic heat equation with Levy noise

Efficient algorithms for wave problems

Gyrokinetic full-f particle-in-cell simulations on open field lines with PICLS

Stability of standing waves for a nonlinear Klein-Gordon equation with delta potentials

Normal approximation of the solution to the stochastic heat equation with Levy noise

The static and dynamic structural heterogeneities of B-DNA: extending Calladine-Dickerson rules

On the density of the supremum of the solution to the linear stochastic heat equation

Local Well-Posedness And Blow-Up For The Half Ginzburg-Landau-Kuramoto Equation With Rough Coefficients And Potential