Density in small time for Lévy processes

Jean Picard

ESAIM: Probability and Statistics (2010)

  • Volume: 1, page 357-389
  • ISSN: 1292-8100

Abstract

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The density of real-valued Lévy processes is studied in small time under the assumption that the process has many small jumps. We prove that the real line can be divided into three subsets on which the density is smaller and smaller: the set of points that the process can reach with a finite number of jumps (Δ-accessible points); the set of points that the process can reach with an infinite number of jumps (asymptotically Δ-accessible points); and the set of points that the process cannot reach by jumping (Δ-inaccessible points).

How to cite

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Picard, Jean. "Density in small time for Lévy processes." ESAIM: Probability and Statistics 1 (2010): 357-389. <http://eudml.org/doc/197726>.

@article{Picard2010,
abstract = { The density of real-valued Lévy processes is studied in small time under the assumption that the process has many small jumps. We prove that the real line can be divided into three subsets on which the density is smaller and smaller: the set of points that the process can reach with a finite number of jumps (Δ-accessible points); the set of points that the process can reach with an infinite number of jumps (asymptotically Δ-accessible points); and the set of points that the process cannot reach by jumping (Δ-inaccessible points). },
author = {Picard, Jean},
journal = {ESAIM: Probability and Statistics},
keywords = {Levy process / small time / density of processes / large deviations'.; Lévy process; jump process; Wiener process; infinitely divisible law},
language = {eng},
month = {3},
pages = {357-389},
publisher = {EDP Sciences},
title = {Density in small time for Lévy processes},
url = {http://eudml.org/doc/197726},
volume = {1},
year = {2010},
}

TY - JOUR
AU - Picard, Jean
TI - Density in small time for Lévy processes
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 1
SP - 357
EP - 389
AB - The density of real-valued Lévy processes is studied in small time under the assumption that the process has many small jumps. We prove that the real line can be divided into three subsets on which the density is smaller and smaller: the set of points that the process can reach with a finite number of jumps (Δ-accessible points); the set of points that the process can reach with an infinite number of jumps (asymptotically Δ-accessible points); and the set of points that the process cannot reach by jumping (Δ-inaccessible points).
LA - eng
KW - Levy process / small time / density of processes / large deviations'.; Lévy process; jump process; Wiener process; infinitely divisible law
UR - http://eudml.org/doc/197726
ER -

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