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Original Articles

Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process

Pages 321-343 | Received 07 Nov 2007, Published online: 23 Feb 2009

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Read on this site (2)

Mark Anthony Caruana. (2019) Non parametric estimation of the measure associated with the Lévy–Khintchine canonical representation. Communications in Statistics - Theory and Methods 48:1, pages 100-111.
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FlorianA.J. Ueltzhöfer & Claudia Klüppelberg. (2011) An oracle inequality for penalised projection estimation of Lévy densities from high-frequency observations. Journal of Nonparametric Statistics 23:4, pages 967-989.
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Articles from other publishers (26)

Céline Duval & Ester Mariucci. (2021) Spectral-free estimation of Lévy densities in high-frequency regime. Bernoulli 27:4.
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Kengo Kato & Daisuke Kurisu. (2020) Bootstrap confidence bands for spectral estimation of Lévy densities under high-frequency observations. Stochastic Processes and their Applications 130:3, pages 1159-1205.
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Émeline Schmisser. (2019) Non parametric estimation of the diffusion coefficients of a diffusion with jumps. Stochastic Processes and their Applications 129:12, pages 5364-5405.
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Liron Ravner, Onno Boxma & Michel Mandjes. (2019) Estimating the input of a Lévy-driven queue by Poisson sampling of the workload process. Bernoulli 25:4B.
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Narayanaswamy Balakrishnan & Chengwei Qin. (2018) Nonparametric evaluation of the first passage time of degradation processes. Applied Stochastic Models in Business and Industry 35:3, pages 571-590.
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Likuan Qin & Viktor Todorov. (2019) Nonparametric implied Lévy densities. The Annals of Statistics 47:2.
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Daisuke Kurisu. (2019) Nonparametric inference on Lévy measures of compound Poisson-driven Ornstein-Uhlenbeck processes under macroscopic discrete observations. Electronic Journal of Statistics 13:2.
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Alberto J. Coca. (2017) Efficient nonparametric inference for discretely observed compound Poisson processes. Probability Theory and Related Fields 170:1-2, pages 475-523.
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Mark Anthony Caruana. (2017) Estimation of Lévy Processes via Stochastic Programming and Kalman Filtering. Methodology and Computing in Applied Probability 19:4, pages 1211-1225.
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Paul Ilhe, Éric Moulines, Francois Roueff & Antoine Souloumiac. (2015) Nonparametric estimation of mark’s distribution of an exponential shot-noise process. Electronic Journal of Statistics 9:2.
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Denis Belomestny, Fabienne Comte, Valentine Genon-Catalot, Hiroki Masuda & Markus ReißFabienne Comte & Valentine Genon-Catalot. 2015. Lévy Matters IV. Lévy Matters IV 77 177 .
Denis Belomestny, Fabienne Comte, Valentine Genon-Catalot, Hiroki Masuda & Markus ReißDenis Belomestny & Markus Reiß. 2015. Lévy Matters IV. Lévy Matters IV 1 76 .
Zhimin Zhang & Hailiang Yang. (2014) Nonparametric estimation for the ruin probability in a Lévy risk model under low-frequency observation. Insurance: Mathematics and Economics 59, pages 168-177.
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Johanna Kappus. (2014) Adaptive nonparametric estimation for Lévy processes observed at low frequency. Stochastic Processes and their Applications 124:1, pages 730-758.
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Fabienne Comte, Céline Duval & Valentine Genon-Catalot. (2013) Nonparametric density estimation in compound Poisson processes using convolution power estimators. Metrika 77:1, pages 163-183.
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Markus Reiß. (2013) Testing the characteristics of a Lévy process. Stochastic Processes and their Applications 123:7, pages 2808-2828.
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Peter J. Brockwell & Eckhard Schlemm. (2013) Parametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations. Journal of Multivariate Analysis 115, pages 217-251.
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Richard Nickl & Markus Reiß. (2012) A Donsker theorem for Lévy measures. Journal of Functional Analysis 263:10, pages 3306-3332.
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Shota Gugushvili. (2012) Nonparametric inference for discretely sampled Lévy processes. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 48:1.
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Jean-Marc Bardet & Donatas Surgailis. (2011) Measuring the roughness of random paths by increment ratios. Bernoulli 17:2.
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Fabienne Comte & Valentine Genon-Catalot. (2011) Estimation for Lévy processes from high frequency data within a long time interval. The Annals of Statistics 39:2.
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Fabienne Comte & Valentine Genon-Catalot. (2010) Non-parametric estimation for pure jump irregularly sampled or noisy Lévy processes. Statistica Neerlandica 64:3, pages 290-313.
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Johanna Kappus & Markus Reiß. (2010) Estimation of the characteristics of a Lévy process observed at arbitrary frequency. Statistica Neerlandica 64:3, pages 314-328.
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Jakob Söhl. (2010) Polar sets for anisotropic Gaussian random fields. Statistics & Probability Letters 80:9-10, pages 840-847.
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Denis Belomestny. (2010) Spectral estimation of the fractional order of a Lévy process. The Annals of Statistics 38:1.
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B. Buchmann. (2010) Weighted empirical processes in the nonparametric inference for Lévy processes. Mathematical Methods of Statistics 18:4, pages 281-309.
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