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We consider a mixed stochastic differential equation driven by possibly dependent fractional Brownian motion and Brownian motion. Under mild regularity assumptions on the coefficients, it is proved that the equation has a unique solution.

Probability · Mathematics 2011-11-09 Yuliya Mishura , Georgiy Shevchenko

In this article we study effects that small perturbations in the noise have to the solution of differential equations driven by H\"older continuous functions of order $H>\frac12$. As an application, we consider stochastic differential…

Probability · Mathematics 2020-05-11 Lauri Viitasaari , Caibin Zeng

In this paper we study a stochastic differential equation driven by a fractional Brownian motion with a discontinuous coefficient. We also give an approximation to the solution of the equation. This is a first step to define a fractional…

Probability · Mathematics 2016-07-25 Johanna Garzón , Jorge A. León , Soledad Torres

We investigate the well-posedness of stochastic differential equations driven by fractional Brownian motion, focusing on the long-range dependent case $H \in (\frac{1}{2}, 1)$. While existing results on regularization by such noise…

Probability · Mathematics 2025-07-01 Maximilian Buthenhoff , Ercan Sönmez

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter…

Probability · Mathematics 2012-03-05 Mireia Besalú , Carles Rovira

In this paper we consider stochastic differential equations with non-negativity constraints, driven by a fractional Brownian motion with Hurst parameter $H>\1/2$. We first study an ordinary integral equation where the integral is defined in…

Probability · Mathematics 2012-03-14 Marco Ferrante , Carles Rovira

In this article, we consider fractional stochastic wave equations on $\mathbb R$ driven by a multiplicative Gaussian noise which is white/colored in time and has the covariance of a fractional Brownian motion with Hurst parameter…

Probability · Mathematics 2019-04-23 Jian Song , Xiaoming Song , Fangjun Xu

In this paper we prove a viability result for multidimensional, time dependent, stochastic differential equations driven by fractional Brownian motion with Hurst parameter1/2 < H < 1, using pathwise approach. The sufficient condition is…

Dynamical Systems · Mathematics 2008-09-01 Ioana Ciotir , Aurel Rascanu

In this paper we show the existence and uniqueness of a solution for a stochastic differential equation driven by an additive noise which is the sum of two fractional Brownian motions with different Hurst parameters. The proofs are based on…

Probability · Mathematics 2022-07-12 David Nualart , Ercan Sönmez

In this article, we present the exact expression of the $L^2$-norm of the forward stochastic integral driven by the multi-dimensional fractional Brownian motion with parameter $\frac{1}{2} < H < 1$. The class of integrands only requires…

Probability · Mathematics 2023-10-26 Alberto Ohashi , Francesco Russo

We present an innovating sensitivity analysis for stochastic differential equations: We study the sensitivity, when the Hurst parameter~$H$ of the driving fractional Brownian motion tends to the pure Brownian value, of probability…

Probability · Mathematics 2017-02-14 Alexandre Richard , Denis Talay

We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H>1/2 and a…

Probability · Mathematics 2022-01-27 João Guerra , David Nualart

In this paper, we focus on the mean-field backward stochastic differential equations (BSDEs) driven by a fractional Brownian motion with Hurst parameter H greater then 1/2. First, the existence and uniqueness of these equations are…

Probability · Mathematics 2017-05-30 Jiaqiang Wen , Yufeng Shi

In this note we prove the existence of a density for the law of the solution for 1-dimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter $H…

Probability · Mathematics 2023-02-09 Mireia Besalú , David Márquez-Carreras , Carles Rovira

In this paper, we study a class of one-dimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H>\ff 1 2$. The drift term of the equation is locally Lipschitz and unbounded in the…

Probability · Mathematics 2019-01-01 Shao-Qin Zhang , Chenggui Yuan

In this paper, we study a conditional distribution dependent stochastic differential equations driven by standard Brownian motion and fractional Brownian motion with Hurst exponent $H>\frac{1}{2}$ simultaneously. First, the existence and…

Probability · Mathematics 2025-05-01 Li Tan , Shengrong Wang

In this paper we study a singular stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter $H>\frac 12$. Under some assumptions on the drift, we show that there is a unique solution, which has…

Probability · Mathematics 2007-11-19 Yaozhong Hu , David Nualart , Xiaoming Song

In this paper, we study the existence and uniqueness of a class of stochastic differential equations driven by fractional Brownian motions with arbitrary Hurst parameter $H\in (0,1)$. In particular, the stochastic integrals appearing in the…

Statistics Theory · Mathematics 2009-09-07 Yu-Juan Jien , Jin Ma

We consider stochastic differential equation $$ d X_t=b(X_t) dt +d W_t^H, $$ where the drift $b$ is either a measure or an integrable function, and $W^H$ is a $d$-dimensional fractional Brownian motion with Hurst parameter $H\in(0,1)$,…

Probability · Mathematics 2025-10-22 Oleg Butkovsky , Khoa Lê , Leonid Mytnik

We prove existence and uniqueness of the solution of a stochastic shell--model. The equation is driven by an infinite dimensional fractional Brownian--motion with Hurst--parameter $H\in (1/2,1)$, and contains a non--trivial coefficient in…

Analysis of PDEs · Mathematics 2014-10-27 Hakima Bessaih , María J. Garrido-Atienza , Björn Schmalfuss
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