67 citations · 185 across the 13 of their papers we have counts for
18 papers
Brownian-time Change of measure
Bobomurod Abdurakhmanov, Hassan Allouba
We prove a fundamental change of measure theorem for the Brownian-time Brownian motion and its associated Brownian-time processes class introduced by Allouba and Zheng in 2001. Thi…
Solving the Kuramoto-Sivashinsky-Burgers equation until the -th dimension: the Brownian-time paradigm
Hassan Allouba
We use our earlier Brownian-time framework to formulate and establish global uniqueness and local-in-time existence of the Burgers incarnation of the Kuramoto-Sivashinsky PDE on $\…
L-Kuramoto-Sivashinsky SPDEs vs. time-fractional SPIDEs: exact continuity and gradient moduli, 1/2-derivative criticality, and laws
Hassan Allouba, Yimin Xiao
We establish exact, dimension-dependent, spatio-temporal, uniform and local moduli of continuity for (1) the fourth order L-Kuramoto-Sivashinsky (L-KS) SPDEs and for (2) the time-f…
L-Kuramoto-Sivashinsky SPDEs in one-to-three dimensions: L-KS kernel, sharp Hölder regularity, and Swift-Hohenberg law equivalence
Hassan Allouba
Generalizing the L-Kuramoto-Sivashinsky (L-KS) kernel from our earlier work, we give a novel explicit-kernel formulation useful for a large class of fourth order deterministic, sto…
Time-fractional and memoryful SIEs on $\Rp\times\Rd$: how far can we push white noise?
Hassan Allouba
High order and fractional PDEs have become prominent in theory and in modeling many phenomena. Here, we focus on the regularizing effect of a large class of memoryful high-order or…
Interacting time-fractional and PDEs systems via Brownian-time and Inverse-stable-Lévy-time Brownian sheets
Hassan Allouba, Erkan Nane
Lately, many phenomena in both applied and abstract mathematics and related disciplines have been expressed in terms of high order and fractional PDEs. Recently, Allouba introduced…