Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 317
Parameter Estimation for Stochastic Partial Differential Equations Driven by an Additive Multi-Order Fractional Brownian Motion
Mohamed El Omari
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 30, 2022
March 03, 2274
April 15, 2274

Abstract: We investigate the parameter estimation problem for a diagonalizable stochastic evolution equation driven by an additive noise that is white in space and fractional in time. The fractional component in the noise is described by the so-called multi- order fractional Brownian motion W^H with Hurst sequence H = (H_1 ,H_2 ,H_3 ,···), introduced in [1]. By using the spectral approach, we study the maximum likelihood estimator as the number of Fourier modes becomes sufficiently large. A necessary and sufficient conditions for consistency and asymptotic normality are presented in terms of ...