LAN property for an ergodic Ornstein–Uhlenbeck process with Poisson jumps

NK Tran - Communications in Statistics-Theory and Methods, 2017 - Taylor & Francis
In this article, we consider an ergodic Ornstein–Uhlenbeck process with jumps driven by a
Brownian motion and a compensated Poisson process, whose drift and diffusion coefficients …

LAN property for an ergodic diffusion with jumps

A Kohatsu-Higa, E Nualart, NK Tran - Statistics, 2017 - Taylor & Francis
In this paper, we consider a multidimensional ergodic diffusion with jumps driven by a
Brownian motion and a Poisson random measure associated with a compound Poisson …

Optimal estimation of the supremum and occupation times of a self-similar Lévy process

J Ivanovs, M Podolskij - Electronic Journal of Statistics, 2022 - projecteuclid.org
In this paper we present new theoretical results on optimal estimation of certain random
quantities based on high frequency observations of a Lévy process. More specifically, we …

Local asymptotic normality for ergodic jump-diffusion processes via transition density approximation

T Ogihara, Y Uehara - Bernoulli, 2023 - projecteuclid.org
Local asymptotic normality for ergodic jump-diffusion processes via transition density
approximation Page 1 Bernoulli 29(3), 2023, 2342–2366 https://doi.org/10.3150/22-BEJ1544 …

Optimal estimation of some random quantities of a L\'evy process

J Ivanovs, M Podolskij - arXiv preprint arXiv:2001.02517, 2020 - arxiv.org
In this paper we present new theoretical results on optimal estimation of certain random
quantities based on high frequency observations of a L\'evy process. More specifically, we …

Time endogeneity and an optimal weight function in pre-averaging covariance estimation

Y Koike - Statistical Inference for Stochastic Processes, 2017 - Springer
We establish a central limit theorem for a class of pre-averaging covariance estimators in a
general endogenous time setting. In particular, we show that the time endogeneity has no …

[HTML][HTML] LAN property for a simple Lévy process

A Kohatsu-Higa, E Nualart, NK Tran - Comptes Rendus Mathematique, 2014 - Elsevier
In this paper, we consider a simple Lévy process given by a Brownian motion and a
compensated Poisson process, whose drift and diffusion parameters as well as its intensity …

Local asymptotic properties for Cox‐Ingersoll‐Ross process with discrete observations

M Ben Alaya, A Kebaier, NK Tran - Scandinavian Journal of …, 2020 - Wiley Online Library
In this paper, we consider a one‐dimensional Cox‐Ingersoll‐Ross (CIR) process whose drift
coefficient depends on unknown parameters. Considering the process discretely observed …

[HTML][HTML] Detecting and estimating intensity of jumps for discretely observed ARMAD (1, 1) processes

D Blanke, D Bosq - Journal of Multivariate Analysis, 2016 - Elsevier
We consider n equidistributed random functions, defined on [0, 1], and admitting fixed or
random jumps, the context being D [0, 1]-valued ARMA (1, 1) processes. We begin with …

LAMN property for jump diffusion processes with discrete observations on a fixed time interval

NK Tran, HL Ngo - Journal of Statistical Planning and Inference, 2023 - Elsevier
We consider a one-dimensional stochastic differential equation with jumps driven by a
Brownian motion and an independent Lévy process with finite Lévy measure, whose drift …