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The order of approximations for solutions of Itô-type stochastic differential equations with jumps. (English) Zbl 1056.60065

Summary: We consider so called strong Taylor approximations for processes, which are solutions of Itô-type SDEs with jumps driven by the homogeneous Poisson process. We give the order of convergence of such approximations in \({\mathcal L}^2\)-norm, that depends on an accepted difference scheme, and show the explicit formula of the order 1 scheme.

MSC:

60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60H05 Stochastic integrals
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)
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[1] DOI: 10.1214/aop/1022855419 · Zbl 0937.60060 · doi:10.1214/aop/1022855419
[2] Kloeden P. E., Numerical Solution of Stochastic Differential Equations (1995) · Zbl 0858.65148
[3] DOI: 10.1007/978-3-662-02619-9 · doi:10.1007/978-3-662-02619-9
[4] Sobczyk K., Stochastic Differential Equations with Applications to Physics and Engineering (1991) · Zbl 0762.60050
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