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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Optimal simulation schemes for Lévy driven stochastic differential equations
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by Arturo Kohatsu-Higa, Salvador Ortiz-Latorre and Peter Tankov PDF
Math. Comp. 83 (2014), 2293-2324 Request permission


We consider a general class of high order weak approximation schemes for stochastic differential equations driven by Lévy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the Lévy process with a high order scheme for the Brownian driven component, applied between the jump times. The overall approximation is analyzed using a stochastic splitting argument. The resulting error bound involves separate contributions of the compound Poisson approximation and of the discretization scheme for the Brownian part, and allows, on one hand, to balance the two contributions in order to minimize the computational time, and on the other hand, to study the optimal design of the approximating compound Poisson process. For driving processes whose Lévy measure explodes near zero in a regularly varying way, this procedure allows us to construct discretization schemes with arbitrary order of convergence for sufficiently regular functionals.
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Additional Information
  • Arturo Kohatsu-Higa
  • Affiliation: Department of Mathematical Sciences and Japan Science and Technology Agency, Ritsumeikan University
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  • Salvador Ortiz-Latorre
  • Affiliation: Department of Mathematics, Centre of Mathematics for Applications, University of Oslo
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  • Peter Tankov
  • Affiliation: LPMA, Univeristy Paris Diderot — Paris 7
  • Email:
  • Received by editor(s): April 22, 2012
  • Received by editor(s) in revised form: November 30, 2012, and January 4, 2013
  • Published electronically: December 17, 2013
  • Additional Notes: The first author acknowledges financial support from the Japanese goverment
    The second author acknowledges financial support from the Catalan government, BP-DGR 2009.
  • © Copyright 2013 American Mathematical Society
  • Journal: Math. Comp. 83 (2014), 2293-2324
  • MSC (2010): Primary 65C30, 60G51
  • DOI:
  • MathSciNet review: 3223333