Related papers: Gamma Noise Analysis
We study stochastic Burgers equation driven by a rough noise $(-\Delta)^{\gamma} dW_t$, where $\Delta$ is the Laplacian in one dimension with Dirichlet boundary conditions, and $\gamma \in [0,1/4)$. We prove exponential estimates for the…
Even though the heat equation with random potential is a well-studied object, the particular case of time-independent Gaussian white noise in one space dimension has yet to receive the attention it deserves. The paper investigates the…
We review properties of confluent functions and the closely related Laguerre polynomials, and determine their bilinear integrals. As is well-known, these integrals are convergent only for a limited range of parameters. However, when one…
We study the existence and propagation of singularities of the solution to a one-dimensional linear stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. Our approach is based on a…
We study nonlinear parabolic stochastic partial differential equations with Wick-power and Wick-polynomial type nonlinearities set in the framework of white noise analysis. These equations include the stochastic Fujita equation, the…
Let $\ce^{*}$ be the space of tempered distributions and $\m$ be the standard Gaussian measure on $\ce^{*}$. Being motivated by the distribution theory on infinite dimensional space by Cochran, Kuo and Sengupta (CKS) \cite{cks}, Asai, Kubo…
We extend Walsh's theory of martingale measures in order to deal with hyperbolic stochastic partial differential equations that are second order in time, such as the wave equation and the beam equation, and driven by spatially homogeneous…
In this paper we give a criterion to prove boundedness results for several operators from $H^1((0,\infty),\gamma_\alpha)$ to $L^1((0,\infty),\gamma_\alpha)$ and also from $L^\infty((0,\infty),\gamma_\alpha)$ to…
We study nonlinear stochastic partial differential equations with Wick-analytic type nonlinearities set in the framework of white noise analysis. These equations include the stochastic Fisher--KPP equations, stochastic Allen--Cahn,…
We study the problem of measurement-induced decoherence using the phase-space approach employing the Gaussian-smoothed Wigner distribution function. Our investigation is based on the notion that measurement-induced decoherence is…
We construct Euclidean random fields $X$ over $\R^d$, by convoluting generalized white noise $F$ with some integral kernels $G$, as $X=G* F$. We study properties of Schwinger (or moment) functions of $X$. In particular, we give a general…
In this article, we consider the stochastic wave equation in spatial dimension $d=1$, with linear term $\sigma(u)=u$ multiplying the noise. This equation is driven by a Gaussian noise which is white in time and fractional in space with…
We first introduce a new model for a two-dimensional gauge-covariant wave equation with space-time white noise. In our main theorem, we obtain the probabilistic global well-posedness of this model in the Lorenz gauge. Furthermore, we prove…
We consider the nonlinear Schr\"odinger equation with multiplicative spatial white noise and an arbitrary polynomial nonlinearity on the two-dimensional full space domain. We prove global well-posedness by using a gauge-transform introduced…
The noise power spectra of spatially extended dynamical systems are investigated, using as a model the Complex Ginzburg-Landau equation with a stochastic term. Analytical and numerical investigations show that the spatial spectra of the…
We study the influence of disorder on propagation of waves in one-dimensional structures. Transmission properties of the process governed by the Schr\"{o}dinger equation with the white noise potential can be expressed through the Lyapunov…
We show that the increments of generalized Wiener process, useful to describe non-Gaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for…
We investigate nonlinear, higher-order dispersive equations with measure (or even less regular) potentials and initial data with low regularity. Our approach is of distributional nature and relies on the phase space analysis (via Gabor wave…
In this article, we consider the following stochastic fractional diffusion equation \begin{equation*} \left(\partial^{\beta}+\dfrac{\nu}{2}\left(-\Delta\right)^{\alpha / 2}\right) u(t, x)= \lambda\: I_{0_+}^{\gamma}\left[u(t, x) \dot{W}(t,…
In this paper, we prove the global wellposedness of the Gross-Pitaevskii equation with white noise potential, i.e. a cubic nonlinear Schr{\"o}dinger equation with harmonic confining potential and spatial white noise multiplicative term.…