Trajectory fitting estimation for stochastic differential equations driven by fractional Brownian motion

Hector Araya; John Barrera

doi:10.1515/rose-2023-2018

Trajectory fitting estimation for stochastic differential equations driven by fractional Brownian motion

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the problem of drift parameter estimation in a stochastic differential equation driven by fractional Brownian motion with Hurst parameter H ϵ (1/2, 1) and small diffusion. The technique that we used is the trajectory fitting method. Strong consistency and asymptotic distribution of the estimator are established as a small diffusion coefficient goes to zero.

Original language	English
Pages (from-to)	339-349
Number of pages	11
Journal	Random Operators and Stochastic Equations
Volume	31
Issue number	4
DOIs	https://doi.org/10.1515/rose-2023-2018
State	Published - 1 Dec 2023
Externally published	Yes

Keywords

Fractional Brownian motion
pathwise integral
stochastic differential equation
trajectory fitting

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title = "Trajectory fitting estimation for stochastic differential equations driven by fractional Brownian motion",

abstract = "We consider the problem of drift parameter estimation in a stochastic differential equation driven by fractional Brownian motion with Hurst parameter H ϵ (1/2, 1) and small diffusion. The technique that we used is the trajectory fitting method. Strong consistency and asymptotic distribution of the estimator are established as a small diffusion coefficient goes to zero.",

keywords = "Fractional Brownian motion, pathwise integral, stochastic differential equation, trajectory fitting",

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AB - We consider the problem of drift parameter estimation in a stochastic differential equation driven by fractional Brownian motion with Hurst parameter H ϵ (1/2, 1) and small diffusion. The technique that we used is the trajectory fitting method. Strong consistency and asymptotic distribution of the estimator are established as a small diffusion coefficient goes to zero.

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KW - pathwise integral

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Trajectory fitting estimation for stochastic differential equations driven by fractional Brownian motion

Abstract

Keywords

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