Wasserstein and total variation distance between marginals of L 'evy\n processes

2017/10/07 by Ester Mariucci, Mariucci, Ester, Markus Reiß +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1710.02715

openalex publication_date 2017/10/07 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We present upper bounds for the Wasserstein distance of order p between the\nmarginals of L 'evy processes, including Gaussian approximations for jumps of\ninfinite activity. Using the convolution structure, we further derive upper\nbounds for the total variation distance between the marginals of L 'evy\nprocesses. Connections to other metrics like Zolotarev and Toscani-Fourier\ndistances are established. The theory is illustrated by concrete examples and\nan application to statistical lower bounds.\n

Cited by

• Multivariate CLT for Lévy processes: convergence rates without moment assumptions
• Efficient estimation of jump parameters for stochastic differential equations driven by Lévy processes
• Ergodicity bounds in the Sliced Wasserstein distance for Schur stable autoregressive processes

Related

• Total variation distance for discretely observed Lévy processes: a Gaussian approximation of the small jumps
• Bounding Kolmogorov distances through Wasserstein and related integral probability metrics
• Evolution of the Wasserstein distance between the marginals of two Markov processes
• Rate estimates for weighted total variation norm in terms of Wasserstein distances
• Estimating processes in adapted Wasserstein distance