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

  • Hector Araya ORCID logo EMAIL logo and John Barrera
Published/Copyright: October 27, 2023

Abstract

We consider the problem of drift parameter estimation in a stochastic differential equation driven by fractional Brownian motion with Hurst parameter H ( 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.

MSC 2020: 60G22; 62M09; 60H3

Communicated by Stanislav Molchanov


Award Identifier / Grant number: 11230051

Award Identifier / Grant number: ECOS210037(C21E07)

Award Identifier / Grant number: AMSUD210023

Funding statement: The first author was partially supported by FONDECYT 11230051, Proyecto ECOS210037(C21E07), Mathamsud AMSUD210023. The work of the second author was supported by a scholarship granted by the Postgraduate and Programs Direction of Universidad Técnica Federico Santa María.

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Received: 2022-10-20
Accepted: 2023-03-20
Published Online: 2023-10-27
Published in Print: 2023-12-01

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