This article attempts to give a short survey of recent progress on a class of elementary
stochastic partial differential equations (for example, stochastic heat equations) driven by …

This paper provides necessary as well as sufficient conditions on the Hurst parameters so
that the continuous time parabolic Anderson model∂ u∂ t= 1 2 Δ+ u W˙ on [0,∞)× R d with …

For the stochastic partial differential equation $\frac {\partial u}{\partial t}=\mathcal L u+ u\dot
W $ where $\dot W $ is Gaussian noise colored in time and $\mathcal L $ is the infinitesimal …

The sample-function regularity of the random-field solution to a stochastic partial differential
equation (SPDE) depends naturally on the roughness of the external noise, as well as on …

We study the well-posedness of a nonlinear one dimensional stochastic heat equation
driven by Gaussian noise:∂ u∂ t=∂ 2 u∂ x 2+ σ (u) W˙, where W˙ is white in time and …

, t> 0, x∈ R, where α> 0, β∈(0, 2], γ≥ 0, λ 0, ν> 0, and W is a Gaussian noise which is white
or fractional in time and rough in space. We prove the existence and uniqueness of the …

In this article, we study the continuity in law of the solutions of two linear multiplicative
SPDEs (the parabolic Anderson model and the hyperbolic Anderson model) with respect to …

In this note, we consider the parabolic Anderson model on R+× R, driven by a Gaussian
noise which is fractional in time with index H 0> 1∕ 2 and fractional in space with index 0< …

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 …

Hölder continuity of stochastic heat equation with rough Gaussian noise - ScienceDirect Skip
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