Wasserstein and total variation distance between marginals of Lévy processes

DOI10.1214/18-EJS1456zbMath1405.60062arXiv1710.02715OpenAlexW2964095789MaRDI QIDQ1657964

Ester Mariucci, Markus Reiss

Publication date: 14 August 2018

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

Full work available at URL: https://arxiv.org/abs/1710.02715

zbMATH Keywords

total variationLévy processesWasserstein distancestatistical lower boundToscani-Fourier distance

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Inference from stochastic processes (62M99)

Related Items (11)

On the role of skewness and kurtosis in tempered stable (CGMY) Lévy models in finance ⋮ Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation ⋮ Stein’s method and approximating the multidimensional quantum harmonic oscillator ⋮ Approximation of Bayesian models for time-to-event data ⋮ Rate-optimal estimation of the Blumenthal-Getoor index of a Lévy process ⋮ Implementable coupling of Lévy process and Brownian motion ⋮ Total variation distance for discretely observed Lévy processes: a Gaussian approximation of the small jumps ⋮ Measuring dependence in the Wasserstein distance for Bayesian nonparametric models ⋮ Wasserstein distance error bounds for the multivariate normal approximation of the maximum likelihood estimator ⋮ Transport distances on random vectors of measures: recent advances in Bayesian nonparametrics ⋮ Total variation distance between a jump-equation and its Gaussian approximation

Cites Work

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• \(L_1\)-distance for additive processes with time-homogeneous Lévy measures
• Nonparametric estimation for Lévy processes from low-frequency observations
• Upper bounds for minimal distances in the central limit theorem
• Testing for jumps in a discretely observed process
• A class of Wasserstein metrics for probability distributions
• Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation.
• Expansion of transition distributions of Lévy processes in small time
• A remark on the rates of convergence for integrated volatility estimation in the presence of jumps
• Distance de Hellinger-Kakutani des lois correspondant à deux processus à accroissements indépendants
• Modern Theory of Summation of Random Variables
• Financial Modelling with Jump Processes
• On Choosing and Bounding Probability Metrics
• Simulation and approximation of Lévy-driven stochastic differential equations
• Coupling distances between Lévy measures and applications to noise sensitivity of SDE
• Optimal Transport
• Introduction to nonparametric estimation

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