Extending the martingale measure stochastic integral with applications to spatially homogeneous spde's
R Dalang - 1999 - projecteuclid.org
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 …
to solve stochastic partial differential equations whose Green's function is not a function but …
Galerkin finite element methods for stochastic parabolic partial differential equations
Y Yan - SIAM journal on numerical analysis, 2005 - SIAM
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 …
driven by nuclear or space-time white noise in the multidimensional case. The discretization …
[图书][B] Stochastic partial differential equations
SV Lototsky, BL Rozovsky - 2017 - Springer
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 …
monograph is supposed to bore rather than batter. The following quotation is attributed to …
[HTML][HTML] Evolution equations driven by a fractional Brownian motion
B Maslowski, D Nualart - Journal of Functional Analysis, 2003 - Elsevier
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 …
a cylindrical fractional Brownian motion with Hurst parameter H> 1 2 and nuclear covariance …
Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency
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 …
where W is a mean zero Gaussian noise and the differential element uW is interpreted both …
Reliability analysis of the uncertain heat conduction model
C Tian, T Jin, X Yang, Q Liu - Computers & Mathematics with Applications, 2022 - Elsevier
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 …
the reliability of products when there are few or no samples. Meanwhile, first hitting time …
Some recent progress on stochastic heat equations
Y Hu - Acta Mathematica Scientia, 2019 - Springer
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 …
stochastic partial differential equations (for example, stochastic heat equations) driven by …
[HTML][HTML] Stochastic integrals for spde's: a comparison
RC Dalang, L Quer-Sardanyons - Expositiones Mathematicae, 2011 - Elsevier
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 …
and various extensions of this theory, alongside of the Da Prato and Zabczyk theory of …
Uncertain partial differential equation with application to heat conduction
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 …
partial differential equations driven by Liu processes. As an application of uncertain partial …
Nonlinear stochastic wave and heat equations
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 …
Wiener process. For the wave equation we consider the cases of d= 1, 2, 3. The heat …