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We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…

Probability · Mathematics 2021-05-26 Xi Chen , Ilya Timofeyev

We study small noise large deviation asymptotics for stochastic differential equations with a multiplicative noise given as a fractional Brownian motion $B^H$ with Hurst parameter $H>\frac12$. The solutions of the stochastic differential…

Probability · Mathematics 2020-06-18 Amarjit Budhiraja , Xiaoming Song

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

We study a two-dimensional incompressible vorticity equation on the torus driven by transport-type fractional Brownian noise with Hurst parameter $H \in (1/2,1)$. The model captures persistent, long-range correlated forcing consistent with…

Probability · Mathematics 2026-04-08 Alexandra Blessing Neamtu , Dan Crisan , Oana Lang

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

We investigate the asymptotic properties of maximum likelihood estimators of the drift parameter for fractional vasicek model driven by a sub-fractional Brownian motion.

Probability · Mathematics 2021-06-08 B. L. S. Prakasa Rao

We study the asymptotic properties of an estimator of Hurst parameter of a stochastic differential equation driven by a fractional Brownian motion with $H > 1/2$. Utilizing the theory of asymptotic expansion of Skorohod integrals introduced…

Probability · Mathematics 2024-07-03 Hayate Yamagishi

We study the two-dimensional fractional Brownian motion with Hurst parameter $H>{1/2}$. In particular, we show, using stochastic calculus, that this process admits a skew-product decomposition and deduce from this representation some…

Probability · Mathematics 2007-05-23 Fabrice Baudoin , David Nualart

In this paper, we will first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk. In order to verify the rationality of this…

Probability · Mathematics 2021-01-11 Chunhao Cai , Qinghua Wang , Weilin Xiao

We investigate the problem of nonparametric estimation of the trend for stochastic differential equations with delay and driven by a fractional Brownian motion through the method of kernel-type estimation for the estimation of a probability…

Probability · Mathematics 2021-04-09 B. L. S. Prakasa Rao

Stochastic differential equations and stochastic dynamics are good models to describe stochastic phenomena in real world. In this paper, we study N independent stochastic processes Xi(t) with real entries and the processes are determined by…

Statistics Theory · Mathematics 2020-01-07 Min Dai , Jinqiao Duan , Junjun Liao , Xiangjun Wang

This paper deals with the Local Asymptotical normality for the joint drift parameter and Hurst parameter $H>3/4$ in the mixed fractional Ornstein-Uhlenbeck process. Different from the only estimation of the drift parameter when $H$ is…

Probability · Mathematics 2025-10-21 Chunhao Cai , Cong Zhang

This paper provides several statistical estimators for the drift and volatility parameters of an Ornstein-Uhlenbeck process driven by fractional Brownian motion, whose observations can be made either continuously or at discrete time…

Probability · Mathematics 2017-03-29 Yaozhong Hu , David Nualart , Hongjuan Zhou

Within the rough path framework we prove the continuity of the solution to random differential equations driven by fractional Brownian motion with respect to the Hurst parameter $H$ when $H \in (1/3, 1/2]$.

Probability · Mathematics 2024-08-27 Francesco C. De Vecchi , Luca M. Giordano , Daniela Morale , Stefania Ugolini

We study the parameter estimation problem of Vasicek Model driven by sub-fractional Brownian processes from discrete observations, and let {S_t^H,t>=0} denote a sub-fractional Brownian motion whose Hurst parameter 1/2<H<1 . The studies are…

Statistics Theory · Mathematics 2020-07-06 Cuiyun Zhang , Jingjun Guo , Aiqin Ma , Bo Peng

Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one parameter and two parameter cases.…

Probability · Mathematics 2007-05-23 Ivan Nourdin , Ciprian A. Tudor

The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of…

Statistics Theory · Mathematics 2024-11-07 Arnab Ganguly

This paper addresses the problem of estimating drift parameter of the Ornstein - Uhlenbeck type process, driven by the sum of independent standard and fractional Brownian motions. The maximum likelihood estimator is shown to be consistent…

Probability · Mathematics 2018-08-03 Pavel Chigansky , Marina Kleptsyna

We study distribution dependent stochastic differential equations with irregular, possibly distributional drift, driven by an additive fractional Brownian motion of Hurst parameter $H\in (0,1)$. We establish strong well-posedness under a…

Probability · Mathematics 2021-06-01 Lucio Galeati , Fabian A. Harang , Avi Mayorcas

We consider a stochastic differential equation with additive fractional noise with Hurst parameter $H>1/2$, and a non-linear drift depending on an unknown parameter. We show the Local Asymptotic Normality property (LAN) of this parametric…

Probability · Mathematics 2017-11-07 Yanghui Liu , Eulalia Nualart , Samy Tindel