We prove a functional stable limit theorem for the discretization error process of a local linearization scheme for stochastic differential equations with additive Brownian noise. The scheme includes the conditional mean of the second-order term involving the Brownian increment in the Taylor expansion of the drift. The leading error is then formed by centered quadratic terms in the Brownian increments, and the sharp normalization is \(n\sqrt n\). Under \(C^3\)-regularity and a Lyapunov-type condition on the drift, the scaled error process converges stably in \(C([0,1],\mathbb R^d)\) to the solution of the limiting linear stochastic differential equation. The martingale part of the limit is driven by a Brownian motion independent of the original \(\sigma\)-field, and its coefficient is determined by the Hessian of the drift and the covariance matrix of the additive noise.
We study the backward-Euler scheme for a class of stochastic functional differential equations (SFDEs) with memory driven by a fractional Brownian motion with Hurst parameter H>1/2. We first establish the local consistency of the method, with a local truncation error of order H -$\rho$- $\beta$ + 1, and then, as the ma...
Alexander Abreu, Lisandro Fermin, E. Mordecki 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 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 prove quantitative pathwise stability estimates for one-dimensional stochastic differential equations driven by a common Brownian motion and a common symmetric $\alpha$-stable process, where $\alpha\in(1,2)$. The comparison is made under a synchronous coupling and is measured by $\sup_{0\le t\le T}\mathbb E|X_t-\wt...
We prove a weighted Wasserstein spectral gap for the three-dimensional primitive equations on $\mathscr E=\{u\in H^1\cap L^8: \partial_zu\in L^4\}$ under finite-rank additive Brownian forcing that is phase-complete finite Fourier and satisfies a quantitative quadratic saturation condition. In particular, four real forc...
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...
Álvaro Guinea Juliá, Alet Roux· 0 citations
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