Approximations for solutions of L\'evy-type stochastic differential equations
Micha{\l} Barski
TL;DR
This paper develops approximation schemes for jump-diffusion equations driven by Lévy processes, extending classical methods like Euler and Milstein to cases with finite and infinite Lévy measures.
Contribution
It generalizes existing approximation schemes for Lévy-type stochastic differential equations, including cases with infinite Lévy measures.
Findings
Constructed strong approximation schemes with specified convergence order.
Extended Euler and Milstein schemes to Lévy processes with infinite measures.
Provided theoretical foundations for approximations of jump-diffusion equations.
Abstract
The problem of the construction of strong approximations with a given order of convergence for jump-diffusion equations is studied. General approximation schemes are constructed for L\'evy type stochastic differential equation. In particular, the paper generalizes the results of Platen Kloeden and Gardo\n. The Euler and the Milstein schemes are shown for finite and infinite L\'evy measure.
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Taxonomy
TopicsStochastic processes and financial applications · Differential Equations and Numerical Methods · Nonlinear Differential Equations Analysis