Establishing pathwise uniqueness for stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H>1/2$ remains challenging, particularly for discontinuous drifts beyond the regularity regimes of existing theories. A canonical example is the sign drift, for which uniqueness fails in the corresponding deterministic equation. In this paper, we complement recent strong existence results by establishing pathwise uniqueness for the equation with sign drift perturbed by fractional Brownian motion for every $H\in(1/2,1)$, thus obtaining strong well-posedness. Our proof develops a new approach based on the infinite iteration of an inequality arising from a fixed-point relation, combined with tail probability estimates exploiting the Gaussian structure of the noise. The methods and results cover a broader class of Gaussian Volterra processes satisfying suitable local nondeterminism and positivity conditions.
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 study stochastic Hamilton--Jacobi--Bellman equations arising from stochastic optimal control problems with random coefficients and possible degenerateness. The viscosity solution is reformulated by using adapted smooth random test fields that touch on stopped space--time neighborhoods almost surely. The state coeffi...
We study a multidimensional nonlinear filtering model whose coefficients depend on a given observation-adapted predictable process and whose observation drift may grow linearly in both the state and the random input. Due to the unboundedness of the observation drift, a global reference measure is not available. To over...
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
We develop an intrinsic well-posedness theory for nonlinear backward stochastic differential equations (BSDEs) driven simultaneously by Brownian motion and a (level-$2$) rough path of finite $p$-variation. Unlike earlier approaches based on smooth approximation or transformation methods, we formulate the equation direc...
P. Friz, Jian Song, Hui-Lin Zhang 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
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