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On tamed euler approximations of sdes driven by levy noise with applications to delay equations
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Univ Edinburgh, Sch Math, Edinburgh EH9 3JZ, Midlothian, Scotland..
Univ Edinburgh, Sch Math, Edinburgh EH9 3JZ, Midlothian, Scotland..
2016 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 54, no 3, 1840-1872 p.Article in journal (Refereed) Published
Abstract [en]

We extend the taming techniques for explicit Euler approximations of stochastic differential equations driven by Levy noise with superlinearly growing drift coefficients. Strong convergence results are presented for the case of locally Lipschitz coefficients. Moreover, rate of convergence results are obtained in agreement with classical literature when the local Lipschitz continuity assumptions are replaced by global assumptions and, in addition, the drift coefficients satisfy polynomial Lipschitz continuity. Finally, we further extend these techniques to the case of delay equations.

Place, publisher, year, edition, pages
2016. Vol. 54, no 3, 1840-1872 p.
Keyword [en]
explicit Euler approximations, rate of convergence, local Lipschitz condition, superlinear growth, SDEs driven by Levy noise, delay equations
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-307465DOI: 10.1137/151004872ISI: 000385026000022OAI: oai:DiVA.org:uu-307465DiVA: diva2:1047337
Available from: 2016-11-17 Created: 2016-11-16 Last updated: 2017-02-20Bibliographically approved

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