Oct 2026· Studies in applied mathematics (Cambridge)· Vol 157· 1 citation· 19 references
Abstract
The purpose of this paper is to introduce a stochastic version of Fokas' unified transform formula for evolution PDEs on domains with boundary. The unified transform method, also known as Fokas method, was originally developed for deterministic initial‐boundary value problems and has, so far, been used primarily in deterministic settings. The modifications introduced here lead to stochastic representation formulas that can be used to define mild solutions of stochastic initial‐boundary value problems and to perform regularity analysis in rough fractional Sobolev spaces, below the algebra threshold. To present the main ideas, we consider the canonical model of linear and nonlinear diffusion equations with additive noise and stochastic boundary conditions in their most elementary form. We assume that the evolution is subject both to external forcing prescribed through Dirichlet‐type Brownian motion and to internal additive forcing whose temporal component is also Brownian.
This paper investigates the averaging behavior of a class of slow–fast fractional stochastic differential equations that incorporate two distinct types of memory effects. The slow variable is governed by a Caputo fractional derivative of order α∈(0,1), and is driven by fractional Brownian motion with a Hurst index H∈(1...
We develop and analyze a Monte Carlo method for sampling killed anomalous diffusions obtained by time-changing Brownian motion with drift by the inverse of a subordinator. The method targets probabilistic representations of time-nonlocal, including time-fractional, Cauchy--Dirichlet problems on bounded domains. Since i...
I. Biočić, Daniel E. Cedeño-Girón, Aleksandar Mijatovic et al.· 0 citations
Fractional Brownian motion provides a useful framework for modeling random phenomena with anti-persistent temporal correlations that arise in applications such as anomalous diffusion, hydrology, finance, and geophysical processes. In this paper, we study a class of semilinear stochastic partial differential equations d...
Antoine Tambue, Aurelien Junior Noupelah, L. Fono· 0 citations
This paper studies a linear stochastic delay differential equation driven by fractional Brownian motion and involving a finite number of discrete delays. The model combines two sources of memory: delayed feedback in the drift and temporal dependence induced by the Hurst parameter of the fractional Brownian motion. We f...
Consider the three-dimensional primitive equations subject to Neumann wind stress driven by finitely many Brownian motions. For arbitrary smooth spatial wind profiles, global pathwise existence and uniqueness without assuming a vertical derivative of the initial datum is proved, extending the local theory of Binz, Hieb...
We study the Cauchy problem for a fractional stochastic evolution equation driven by a cylindrical Wiener process, in which the time derivative is understood in the Caputo sense of order q ∈ (0, 1) and the noise enters through a Riemann–Liouville fractional integral. After collecting the required notions on progressive...
Ilolov Mamadsho, Elnazarov Addis A, Munosibshoev Jovid· Global and Stochastic Analys...· 0 citations
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