Statistical inference for time-changed Lévy processes via Mellin transform approach

D. Belomestny; Schoenmakers J.

doi:10.1016/j.spa.2016.01.005

Публикации

?

Statistical inference for time-changed Lévy processes via Mellin transform approach

Stochastic Processes and their Applications. 2016. Vol. 126. No. 7. P. 2092–2122.

Беломестный Д. В., Schoenmakers J.

Given a Lévy process (Lt)t≥0 and an independent nondecreasing process (time change) (T(t))t≥0, we consider the problem of statistical inference on T based on low-frequency observations of the time-changed Lévy process LT(t). Our approach is based on the genuine use of Mellin and Laplace transforms. We propose a consistent estimator for the density of the increments of T in a stationary regime, derive its convergence rates and prove the optimality of the rates. It turns out that the convergence rates heavily depend on the decay of the Mellin transform of T. Finally, the performance of the estimator is analysed via a Monte Carlo simulation study.

Язык: английский

DOI

Текст на другом сайте

Ключевые слова: time-changed Levy process Mellin transform Laplace transform Low-frequency observations

ПУБЛИКАЦИЯ ПОДГОТОВЛЕНА ПО РЕЗУЛЬТАТАМ ПРОЕКТА:

Вероятностные и статистические методы анализа сложных моделей, задаваемых стохастическими дифференциальными и разностными уравнениями (2016)

Nonparametric statistical inference for compound models

Беломестный Д. В., Морозова Е. А., Панов В. А., Statistics 2024 Vol. 58 No. 4 P. 943–960

Добавлено: 21 августа 2024 г.

Limit Distributions in Stochastic Networks with Message-Passing Synchronization

Манита А. Д., , in: Analytical and Computational Methods in Probability TheoryVol. 10684: Analytical and Computational Methods in Probability Theory.: Berlin: Springer, 2017. P. 347–360.

Добавлено: 16 июля 2018 г.

Optimal Antivirus Protection Strategy in Computer Networks

Гришунина Ю. Б., Манита Л. А., , in: Analytical and Computational Methods in Probability TheoryVol. 10684: Analytical and Computational Methods in Probability Theory.: Berlin: Springer, 2017. P. 75–82.

Добавлено: 2 июля 2018 г.

A Model for Network Virus Protection Based on Regenerative Process

Yu. Grishunina, L. Manita, , in: Analytical and computational methods in probability theory and its applications (ACMPT-2017). Proceedings of the International Scientific Conference.: M.: RUDN, 2017. P. 80–84.

Добавлено: 20 июня 2018 г.

Multivariate subordination of stable processes

Панов В. А., Самарин Е. А., / Series arXiv "math". 2018. No. 1802.02876.

Добавлено: 9 февраля 2018 г.

Semiparametric estimation in the normal variance-mean mixture model

Беломестный Д. В., Панов В. А., Statistics 2018 Vol. 52 No. 3 P. 571–589

Добавлено: 19 января 2018 г.

Optimal Antivirus Protection Strategy in Computer Networks

Гришунина Ю. Б., Манита Л. А., Lecture Notes in Computer Science 2017 Vol. 10684 P. 75–82

Добавлено: 22 декабря 2017 г.

Low-frequency estimation of continuous-time moving average Levy processes

Беломестный Д. В., Панов В. А., Woerner J., Bernoulli: a journal of mathematical statistics and probability 2019 Vol. 25 No. 2 P. 902–931

Добавлено: 9 декабря 2017 г.

Generalized Post–Widder inversion formula with application to statistics

Беломестный Д. В., Mai H., Schoenmakers J., Journal of Mathematical Analysis and Applications 2017 No. 455 P. 89–104

Добавлено: 22 сентября 2017 г.

Semiparametric estimation in the normal variance-mean mixture model

Беломестный Д. В., Панов В. А., / Series ArXiv.org "Stat". 2017. No. 1705.07578.

Добавлено: 23 мая 2017 г.

Low frequency estimation of continuous-time moving average Lévy processes

Беломестный Д. В., Панов В. А., Woerner J., / Series arXiv "math". 2016. No. 1607.00896.

Добавлено: 5 июля 2016 г.

Telegraph process in the bounded domain with absorbing lower boundary and reflecting with delay upper boundary

Поспелов И. Г., Радионов С. А., / Series arXiv "math". 2015. No. 1509.06945.

Добавлено: 22 октября 2015 г.

Statistical inference for generalized Ornstein-Uhlenbeck processes

Беломестный Д. В., Панов В. А., Electronic journal of statistics 2015 Vol. 9 No. 2 P. 1974–2006

In this paper, we consider the problem of statistical inference for generalized Ornstein-Uhlenbeck processes of the type \[ X_{t} = e^{-\xi_{t}} \left( X_{0} + \int_{0}^{t} e^{\xi_{u-}} d u \right), \] where \(\xi_s\) is a L{\'e}vy process. Our primal goal is to estimate the characteristics of the L\'evy process \(\xi\) from the low-frequency observations of the process \(X\). We present ...

Добавлено: 1 сентября 2015 г.

Series representations for multivariate time-changed Levy models

Панов В. А., Methodology and Computing in Applied Probability 2017 Vol. 19 No. 1 P. 97–119

In this paper, we analyze a Lévy model based on two popular concepts - subordination and Lévy copulas. More precisely, we consider a two-dimensional Lévy process such that each component is a time-changed (subordinated) Brownian motion and the dependence between subordinators is described via some Lévy copula. The main result of this paper is the ...

Добавлено: 31 августа 2015 г.

Statistical Skorohod embedding problem: Optimality and asymptotic normality

Беломестный Д. В., Schoenmakers J., Statistics and Probability Letters 2015 Vol. 104 P. 169–180

Given a Brownian motion B, we consider the so-called statistical Skorohod embedding problem of recovering the distribution of an independent random time T based on i.i.d. sample from BT. We propose a consistent estimator for the density of T, derive its convergence rates and prove their optimality. ...

Добавлено: 28 июля 2015 г.

Series representations for bivariate time-changed Levy models

Панов В. А., Сироткин И. Н., / Series math "arxiv.org". 2015. No. 1503.02214.

Добавлено: 10 марта 2015 г.