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

DOI10.1214/21-EJS1928zbMath1493.62501OpenAlexW4210547891MaRDI QIDQ2136630

Mark Podolskij, Jevgenijs Ivanovs

Publication date: 11 May 2022

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-16/issue-1/Optimal-estimation-of-the-supremum-and-occupation-times-of-a/10.1214/21-EJS1928.full

zbMATH Keywords

Lévy processesself-similaritylocal timeoccupation timeoptimal estimationsupremumconditioning to stay positiveweak limit theorems

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05) Nonparametric tolerance and confidence regions (62G15) Markov processes: estimation; hidden Markov models (62M05) Self-similar stochastic processes (60G18)

Related Items (2)

Optimal \(L^2\)-approximation of occupation and local times for symmetric stable processes ⋮ Central limit theorems for discretized occupation time functionals

Uses Software

• SupStable.jl

Cites Work

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• Making and Evaluating Point Forecasts
• On the law of the supremum of Lévy processes
• Asymptotic lower bounds in estimating jumps
• Discretization of processes.
• Splitting at the infimum and excursions in half-lines for random walks and Lévy processes
• Explicit formula for the supremum distribution of a spectrally negative stable process
• Proof of the law of iterated logarithm through diffusion equation
• On Lévy processes conditioned to stay positive
• The upper envelope of positive self-similar Markov Processes
• On the character of convergence to Brownian local time. II
• On mixing and stability of limit theorems
• Rates of convergence to the local time of a diffusion
• Zooming in on a Lévy process at its supremum
• Discretization error in simulation of one-dimensional reflecting Brownian motion
• On the discrete approximation of occupation time of diffusion processes
• Approximation of occupation time functionals
• Discretization error for a two-sided reflected Lévy process
• Zooming-in on a Lévy process: failure to observe threshold exceedance over a dense grid
• The asymptotic behavior of densities related to the supremum of a stable process
• An infinite dimensional convolution theorem with applications to the efficient estimation of the integrated volatility
• Inversion of the space and time of stable Lévy processes
• Parametric Estimation of Lévy Processes
• On the Optimality of Conditional Expectation as a Bregman Predictor
• The joint density of the maximum and its location for a Wiener process with drift
• On estimating the diffusion coefficient from discrete observations
• Exact simulation of the extrema of stable processes
• Drift Parameter Estimation for a Reflected Fractional Brownian Motion Based on its Local Time
• Conditioned stable Lévy processes and the Lamperti representation
• Maxima of sums of random variables and suprema of stable processes

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