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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Nonlinear Lévy processes and their characteristics
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by Ariel Neufeld and Marcel Nutz PDF
Trans. Amer. Math. Soc. 369 (2017), 69-95 Request permission

Abstract:

We develop a general construction for nonlinear Lévy processes with given characteristics. More precisely, given a set $\Theta$ of Lévy triplets, we construct a sublinear expectation on Skorohod space under which the canonical process has stationary independent increments and a nonlinear generator corresponding to the supremum of all generators of classical Lévy processes with triplets in $\Theta$. The nonlinear Lévy process yields a tractable model for Knightian uncertainty about the distribution of jumps for which expectations of Markovian functionals can be calculated by means of a partial integro-differential equation.
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Additional Information
  • Ariel Neufeld
  • Affiliation: Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
  • MR Author ID: 1028695
  • Email: ariel.neufeld@math.ethz.ch
  • Marcel Nutz
  • Affiliation: Departments of Statistics and Mathematics, Columbia University, New York, New York 10027
  • MR Author ID: 912101
  • Email: mnutz@columbia.edu
  • Received by editor(s): January 28, 2014
  • Received by editor(s) in revised form: November 29, 2014
  • Published electronically: March 9, 2016
  • Additional Notes: The first author gratefully acknowledges the financial support of Swiss National Science Foundation Grant PDFMP2-137147/1
    The second author gratefully acknowledges the financial support of NSF Grant DMS-1208985
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 69-95
  • MSC (2010): Primary 60G51, 60G44, 93E2
  • DOI: https://doi.org/10.1090/tran/6656
  • MathSciNet review: 3557768