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In this paper, we investigate the optimal strong convergence rate of numerical approximations for the Cox--Ingersoll--Ross model driven by fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. To deal with the difficulties caused…

Numerical Analysis · Mathematics 2020-04-17 Jialin Hong , Chuying Huang , Minoo Kamrani , Xu Wang

We give a new take on the error analysis of approximations of stochastic differential equations (SDEs), utilizing and developing the stochastic sewing lemma of L\^e (2020). This approach allows one to exploit regularization by noise effects…

Probability · Mathematics 2021-08-10 Oleg Butkovsky , Konstantinos Dareiotis , Máté Gerencsér

We study the weak approximation error of a skew diffusion with bounded measurable drift and H\"older diffusion coefficient by an Euler-type scheme, which consists of iteratively simulating skew Brownian motions with constant drift. We first…

Probability · Mathematics 2016-09-30 Noufel Frikha

We consider stochastic differential equation involving pathwise integral with respect to fractional Brownian motion. The estimates for the Hurst parameter are constructed according to first- and second-order quadratic variations of observed…

Probability · Mathematics 2012-06-28 K. Kubilius , Y. Mishura

In this paper, by using Girsanov's transformation and the property of the corresponding reference stochastic differential equations, we investigate weak existence and uniqueness of solutions and weak convergence of Euler-Maruyama scheme to…

Probability · Mathematics 2019-07-05 Yongqiang Suo , Chenggui Yuan , shaoqin Zhang

We study the strong approximation of stochastic differential equations with discontinuous drift coefficients and (possibly) degenerate diffusion coefficients. To account for the discontinuity of the drift coefficient we construct an…

Numerical Analysis · Mathematics 2019-04-25 Andreas Neuenkirch , Michaela Szölgyenyi , Lukasz Szpruch

We are interested in the time discretization of stochastic differential equations with additive d-dimensional Brownian noise and L q -- L $\rho$ drift coefficient when the condition d $\rho$ + 2 q < 1, under which Krylov and R{\"o}ckner…

Probability · Mathematics 2021-05-12 Benjamin Jourdain , Stéphane Menozzi

We consider equidistant approximations of stochastic integrals driven by H\"older continuous Gaussian processes of order $H>\frac12$ with discontinuous integrands involving bounded variation functions. We give exact rate of convergence in…

Probability · Mathematics 2022-09-15 Ehsan Azmoodeh , Pauliina Ilmonen , Nourhan Shafik , Tommi Sottinen , Lauri Viitasaari

We consider the time discretization of fractional stochastic wave equation with Gaussian noise, which is negatively correlated. Major obstacles to design and analyze time discretization of stochastic wave equation come from the…

Numerical Analysis · Mathematics 2022-05-20 Xing Liu

This paper establishes a discretization scheme for a large class of stochastic differential equations driven by a time-changed Brownian motion with drift, where the time change is given by a general inverse subordinator. The scheme involves…

Probability · Mathematics 2015-11-13 Ernest Jum , Kei Kobayashi

In a previous paper, we studied the ergodic properties of an Euler scheme of a stochastic differential equation with a Gaussian additive noise in order to approximate the stationary regime of such equation. We now consider the case of…

Probability · Mathematics 2013-11-20 Serge Cohen , Fabien Panloup , Samy Tindel

In this article, an uniform discretization of stochastic integrals $\int_{0}^{1} f'_-(B_t)\ud B_t$, with respect to fractional Brownian motion with Hurst parameter $H \in (1/2,1)$, for a large class of convex functions $f$ is considered. In…

Probability · Mathematics 2014-12-08 Lauri Viitasaari , Ehsan Azmoodeh

In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters $H_{1}, H_{2}…

Numerical Analysis · Mathematics 2022-01-27 Daxin Nie , Jing Sun , Weihua Deng

Here, we provide a unified framework for numerical analysis of stochastic nonlinear fractional diffusion equation driven by fractional Gaussian noise with Hurst index $H\in(0,1)$. A novel estimate of the second moment of the stochastic…

Numerical Analysis · Mathematics 2021-04-29 Daxin Nie , Weihua Deng

In this paper, we consider the problem of estimating the drift parameter of solution to the stochastic differential equation driven by a fractional Brownian motion with Hurst parameter less than $1/2$ under complete observation. We derive a…

Statistics Theory · Mathematics 2018-07-11 Kohei Chiba

In this paper, we establish the weak convergence rate of density-dependent stochastic differential equations with bounded drift driven by $\alpha$-stable processes with $\alpha\in(1,2)$. The well-posedness of these equations has been…

Probability · Mathematics 2024-06-03 Ke Song , Zimo Hao

In this paper, we establish the theory of chaos propagation and propose an Euler-Maruyama scheme for McKean-Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst exponent $H \in (0,1)$. Meanwhile, upper…

Numerical Analysis · Mathematics 2022-09-13 Jie He , Shuaibin Gao , Weijun Zhan , Qian Guo

The stochastic Cahn-Hilliard equation driven by a fractional Brownian sheet provides a more accurate model for correlated space-time random perturbations. This study delves into two key aspects: first, it rigorously examines the regularity…

Numerical Analysis · Mathematics 2026-02-16 Nan Deng , Wanrong Cao

In the present article we study strong approximation of solutions of scalar stochastic differential equations (SDEs) with bounded and $\alpha$-H\"older continuous drift coefficient and constant diffusion coefficient at time point $1$.…

Probability · Mathematics 2025-04-30 Simon Ellinger , Thomas Müller-Gronbach , Larisa Yaroslavtseva

The purpose of this paper is to establish the convergence in distribution of the normalized error in the Euler approximation scheme for stochastic Volterra equations driven by a standard Brownian motion, with a kernel of the form…

Probability · Mathematics 2022-04-18 David Nualart , Bhargobjyoti Saikia