We extend the definition of Walsh's martingale measure stochastic integral so as to be able
to solve stochastic partial differential equations whose Green's function is not a function but …

We study the finite element method for stochastic parabolic partial differential equations
driven by nuclear or space-time white noise in the multidimensional case. The discretization …

There are textbooks and there are research monographs. Some believe that a research
monograph is supposed to bore rather than batter. The following quotation is attributed to …

In this paper we study nonlinear stochastic evolution equations in a Hilbert space driven by
a cylindrical fractional Brownian motion with Hurst parameter H> 1 2 and nuclear covariance …

This paper studies the stochastic heat equation with multiplicative noises of the form uW,
where W is a mean zero Gaussian noise and the differential element uW is interpreted both …

Uncertainty theory has been demonstrated as a rigorous mathematical system to measure
the reliability of products when there are few or no samples. Meanwhile, first hitting time …

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 …

We present the Walsh theory of stochastic integrals with respect to martingale measures,
and various extensions of this theory, alongside of the Da Prato and Zabczyk theory of …

This paper first presents a tool of uncertain partial differential equation, which is a type of
partial differential equations driven by Liu processes. As an application of uncertain partial …

We study nonlinear wave and heat equations on ℝ d driven by a spatially homogeneous
Wiener process. For the wave equation we consider the cases of d= 1, 2, 3. The heat …