English
Related papers

Related papers: Almost Sure Averaging for Evolution Equations driv…

200 papers

This paper discusses a new type of anticipated backward stochastic differential equation with a time-delayed generator (DABSDEs, for short) driven by fractional Brownian motion, also known as fractional BSDEs, with Hurst parameter…

Probability · Mathematics 2023-05-24 Pei Zhang , Nur Anisah Mohamed , Adriana Irawati Nur Ibrahim

In this article, we study the numerical approximation of stochastic differential equations driven by a multidimensional fractional Brownian motion (fBm) with Hurst parameter greater than 1/3. We introduce an implementable scheme for these…

Probability · Mathematics 2015-05-18 Aurélien Deya , Andreas Neuenkirch , Samy Tindel

The sub-fractional Brownian motion (sfBm) is a stochastic process, characterized by non-stationarity in their increments and long-range dependency, considered as an intermediate step between the standard Brownian motion (Bm) and the…

Mathematical Finance · Quantitative Finance 2021-04-09 Axel A. Araneda , Nils Bertschinger

We present a new simple method for rounding a semidefinite programming relaxation of a constraint satisfaction problem. We apply it to the problem of approximate angular synchronization. Specifically, we are given directed distances on a…

Data Structures and Algorithms · Computer Science 2018-12-11 Kevin L. Chang , Alantha Newman

In certain applications, for instance biomechanics, turbulence, finance, or Internet traffic, it seems suitable to model the data by a generalization of a fractional Brownian motion for which the Hurst parameter $H$ is depending on the…

Statistics Theory · Mathematics 2007-06-13 Jean-Marc Bardet , Pierre Bertrand

Stochastic differential equations are widely used in various fields; in particular, the usefulness of duality relations has been demonstrated in some models such as population models and Brownian momentum processes. In this study, a…

Statistical Mechanics · Physics 2021-02-09 Jun Ohkubo

Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most recent and most general family is based on the fractional…

Probability · Mathematics 2025-07-23 Christian Bender , Yana A. Butko , Mirko D'Ovidio , Gianni Pagnini

In this paper, we focus on mean-field anticipated backward stochastic differential equations (MF-BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H>1/2. First, the existence and uniqueness of this new type of…

Probability · Mathematics 2018-05-23 Soukaina Douissi , Jiaqiang Wen , Yufeng Shi

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

Stochastic dynamics of a quantum system driven by $N$ statistically independent random sudden quenches in a fixed time interval is studied. We reveal that with growing $N$ the system approaches a deterministic limit indicating…

Quantum Physics · Physics 2018-08-15 Marcin Łobejko , Jerzy Dajka , Jerzy Łuczka

Fractional stochastic volatility models have been widely used to capture the non-Markovian structure revealed from financial time series of realized volatility. On the other hand, empirical studies have identified scales in stock price…

Mathematical Finance · Quantitative Finance 2019-01-25 Jean-Pierre Fouque , Ruimeng Hu

In this paper we prove, for small Hurst parameters, the higher order differentiability of a stochastic flow associated with a stochastic differential equation driven by an additive multi-dimensional fractional Brownian noise, where the…

Probability · Mathematics 2018-05-15 Oussama Amine , David R. Baños , Frank Proske

This article is concerned with stochastic differential equations driven by a $d$ dimensional fractional Brownian motion with Hurst parameter $H>1/4$, understood in the rough paths sense. Whenever the coefficients of the equation satisfy a…

Probability · Mathematics 2019-07-02 Xi Geng , Cheng Ouyang , Samy Tindel

We develop a GMM approach for estimation of log-normal stochastic volatility models driven by a fractional Brownian motion with unrestricted Hurst exponent. We show that a parameter estimator based on the integrated variance is consistent…

Statistical Finance · Quantitative Finance 2026-01-16 Anine E. Bolko , Kim Christensen , Mikko S. Pakkanen , Bezirgen Veliyev

We consider Riemann sum approximations of stochastic integrals with respect to the fractional Browian motion of index $H\geq \frac12$. We show the convergence of these schemes at first and second order. The processes obtained in the limit…

Probability · Mathematics 2021-12-20 Valentin Garino , Ivan Nourdin , Pierre Vallois

The numerical analysis of stochastic time fractional evolution equations presents considerable challenges due to the limited regularity of the model caused by the nonlocal operator and the presence of noise. The existing time-stepping…

Numerical Analysis · Mathematics 2024-01-22 Minghua Chen , Jiankang Shi , Zhen Song , Yubin Yan , Zhi Zhou

Stochastic calculus with respect to fractional Brownian motion (fBm) has attracted a lot of interest in recent years, motivated in particular by applications in finance and Internet traffic modeling. Multifractional Brownian motion (mBm) is…

Probability · Mathematics 2011-03-29 Joachim Lebovits , Jacques Lévy Vehel

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

This paper reviews and extends some recent results on the multivariate fractional Brownian motion (mfBm) and its increment process. A characterization of the mfBm through its covariance function is obtained. Similarly, the correlation and…

We establish almost sure invariance principles, a strong form of approximation by Brownian motion, for non-stationary time-series arising as observations on dynamical systems. Our examples include observations on sequential expanding maps,…

Dynamical Systems · Mathematics 2014-06-18 N. Haydn , M. Nicol , A. Tôrôk , S. Vaienti