67 citations · 185 across the 13 of their papers we have counts for
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Applications of the quadratic covariation differentiation theory: variants of the Clark-Ocone and Stroock's formulas
Hassan Allouba, Ramiro Fontes
In a 2006 article (\cite{A1}), Allouba gave his quadratic covariation differentiation theory for Itô's integral calculus. He defined the derivative of a semimartingale with respect…
From Brownian-time Brownian sheet to a fourth order and a Kuramoto-Sivashinsky-variant interacting PDEs systems
Hassan Allouba
We introduce -parameter $\Rd$-valued Brownian-time Brownian sheet (BTBS): a Brownian sheet where each "time" parameter is replaced with the modulus of an independent Brownian mo…
A Differentiation Theory for Itô's Calculus
Hassan Allouba
A peculiar feature of Itô's calculus is that it is an integral calculus that gives no explicit derivative with a systematic differentiation theory counterpart, as in elementary cal…
Semimartingale attractors for Allen-Cahn SPDEs driven by space-time white noise I: Existence and finite dimensional asymptotic behavior
Hassan Allouba, Jose A. Langa
We delve deeper into the study of semimartingale attractors that we recently introduced in Allouba and Langa \cite{AL0}. In this article we focus on second order SPDEs of the Allen…
SDDEs limits solutions to sublinear reaction-diffusion SPDEs
Hassan Allouba
We start by introducing a new definition of solutions to heat-based SPDEs driven by space-time white noise: SDDEs (stochastic differential-difference equations) limits solutions. I…
A linearized Kuramoto-Sivashinsky PDE via an imaginary-Brownian-time-Brownian-angle process
Hassan Allouba
We introduce a new imaginary-Brownian-time-Brownian-angle process, which we also call the linear-Kuramoto-Sivashinsky process (LKSP). Building on our techniques in two recent artic…