Parameter estimation for fractional power type diffusion: A hybrid Bayesian-deep learning approach

被引：0

作者：

Araya, Hector ^{[1
]}

Plaza-Vega, Francisco ^{[2
]}

机构：

[1] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Penalolen, Chile

[2] Univ Santiago Chile, Santiago, Chile

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2024年 / 53卷 / 22期

关键词：

Parameter estimation; power-type fractional diffusion; fractional Brownian motion; ABC; DIFFERENTIAL-EQUATIONS; NEURAL-NETWORKS; INFERENCE; DRIVEN;

D O I：

10.1080/03610926.2023.2280522

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this article, we consider the problem of parameter estimation in a power-type diffusion driven by fractional Brownian motion with Hurst parameter in (1/2,1). To estimate the parameters of the process, we use an approximate bayesian computation method. Also, a particular case is addressed by means of variations and wavelet-type methods. Several theoretical properties of the process are studied and numerical examples are provided in order to show the small sample behavior of the proposed methods.

引用

页码：8234 / 8254

页数：21

共 41 条

[1] Bayesian Inference on the Memory Parameter for Gamma-Modulated Regression Models [J].

Andrade, Plinio ;

Rifo, Laura ;

Torres, Soledad ;

Torres-Aviles, Francisco .

ENTROPY, 2015, 17 (10) :6576-6597

[2]

Belfadli R., 2011, FRONTIERS SCI ENG, V1, P1

[3] Bayesian inference for partially observed stochastic differential equations driven by fractional Brownian motion [J].

Beskos, A. ;

Dureau, J. ;

Kalogeropoulos, K. .

BIOMETRIKA, 2015, 102 (04) :809-827

[4]

Cybenko G., 1989, Mathematics of Control, Signals, and Systems, V2, P303, DOI 10.1007/BF02551274

[5] Hurst Index Estimation in Stochastic Differential Equations Driven by Fractional Brownian Motion [J].

Gairing, Jan ;

Imkeller, Peter ;

Shevchenko, Radomyra ;

Tudor, Ciprian .

JOURNAL OF THEORETICAL PROBABILITY, 2020, 33 (03) :1691-1714

[6]

Geron A., 2019, Hands-on Machine Learning with Scikit-Learn, Keras and TensorFlow

[7] Estimation of the Hurst parameter from discrete noisy data [J].

Gloter, Arnaud ;

Hoffmann, Marc .

ANNALS OF STATISTICS, 2007, 35 (05) :1947-1974

[8]

Goodfellow I, 2016, ADAPT COMPUT MACH LE, P1

[9] A Bayesian Approach to Estimating the Long Memory Parameter [J].

Holan, Scott ;

McElroy, Tucker ;

Chakraborty, Sounak .

BAYESIAN ANALYSIS, 2009, 4 (01) :159-190

[10] MULTILAYER FEEDFORWARD NETWORKS ARE UNIVERSAL APPROXIMATORS [J].

HORNIK, K ;

STINCHCOMBE, M ;

WHITE, H .

NEURAL NETWORKS, 1989, 2 (05) :359-366

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