arXiv 2201.003722022-01-02math.STstat.TH

Parameter estimation of stochastic differential equation driven by small fractional noise

Shohei Nakajima, Yasutaka Shimizu

英文摘要：

We study the problem of parametric estimation for continuously observed stochastic processes driven by additive small fractional Brownian motion with Hurst index 0<H<1/2 and 1/2<H<1. Under some assumptions on the drift coefficient, we obtain the asymptotic normality and moment convergence of maximum likelihood estimator of the drift parameter .

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Nonparametric Estimation for Stochastic Differential Equations Driven by Fractional Brownian Motion

We study the nonparametric Nadaraya-Watson estimator of the drift function for ergodic stochastic processes driven by fractional Brownian motion of Hurst parameter H > 1/2. The estimator is based on the discretely observed stochastic processes. By using the ergodic properties and stochastic integral, we obtain the consistency of the proposed estimator.

2022-04-30math.STstat.MEstat.TH

Maximum likelihood estimation for stochastic differential equations driven by a mixed fractional Brownian motion with random effects

We discuss maximum likelihood estimation of parameters for models governed by a stochastic differential equation driven by a mixed fractional Brownian motion with random effects.

2021-04-30math.PRmath.STstat.TH

Least squares estimators for discretely observed stochastic processes driven by small fractional noise

We study the problem of parameter estimation for discretely observed stochastic differential equations driven by small fractional noise. Under some conditions, we obtain strong consistency and rate of convergence of the least square estimator(LSE) when small dispersion coefficient converges to 0 and sample size converges to infty.

2022-01-20math.STstat.TH

A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise

We study a least square-type estimator for an unknown parameter in the drift coefficient of a stochastic differential equation with additive fractional noise of Hurst parameter H>1/2. The estimator is based on discrete time observations of the stochastic differential equation, and using tools from ergodic theory and stochastic analysis we derive its strong consistency.

2011-11-08math.PRmath.STstat.TH

Order estimate of functionals related to fractional Brownian motion and asymptotic expansion of the quadratic variation of fractional stochastic differential equation

We derive an asymptotic expansion for the quadratic variation of a stochastic process satisfying a stochastic differential equation driven by a fractional Brownian motion, based on the theory of asymptotic expansion of Skorohod integrals converging to a mixed normal limit. In order to apply the general theory, it is necessary to estimate functionals that are a randomly weighted sum of products of multiple integrals of the fractional Brownian motion, in expanding the quadratic variation and identifying the limit random symbols. To overcome the difficulty, we introduce two types of exponents by …

2022-06-01math.PRmath.STstat.TH

Stochastic integration for fractional Levy process and stochastic differential equation driven by fractional Levy noise

In this paper, based on the white noise analysis of square integrable pure-jump Levy process given by [1], we define the formal derivative of fractional Levy process defined by the square integrable pure-jump Levy process as the fractional Levy noises by considering fractional Levy process as the generalized functional of Levy process, and then we define the Skorohod integral with respect to the fractional Levy process. Moreover, we propose a class of stochastic Volterra equations driven by fractional Levy noises and investigate the existence and uniqueness of their solutions; In addition, we …

2013-07-16math-phmath.DSmath.MP

更多相关论文收起更多论文

Stochastic Partial Differential Equations Driven by Fractional Levy Noises

In this paper, we investigate stochastic partial differential equations driven by multi-parameter anisotropic fractional Levy noises, including the stochastic Poisson equation, the linear heat equation, and the quasi-linear heat equation. Well-posedness of these equations under the fractional noises will be addressed. The multi-parameter anisotropic fractional Levy noise is defined as the formal derivative of the anisotropic fractional Levy random field. In doing so, there are two folds involved. First, we consider the anisotropic fractional Levy random field as the generalized functional of t…

2014-10-03math-phmath.APmath.DS