Abstract
<abstract><p>Davie defined a Levy variant and the combination of single random variables to ensure that the diffusion matrix did not degenerate. The use of the method proposed by Davie, which is a combination of the Euler method and the exact combination, was investigated for applying the degenerate Levy diffusion approach to $ \big(B_{ik}(Y)\big) $. We use certain degenerate conditions of diffusion which contribute to order convergence. We also show MATLAB codes to apply the integrated solution to an SDE and observe a convergence behavior. We also evaluate the agreement between the theoretical values and the MATLAB numerical example.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference19 articles.
1. Y. Alnafisah, The exact coupling with trivial coupling (combined method) in two-dimensional sde with non-invertiblity matrix, Dyn. Syst. Appl., 28 (2019), 111–142.
2. A. M. Davie, Pathwise approximation of stochastic differential equations using coupling, unpublished work.
3. P. E. Kloeden, E. Platen, Numerical solution of stochastic differential equations, Springer-Verlag, 1992. https://doi.org/10.1007/978-3-662-12616-5
4. M. Wiktorsson, Joint characteristic function and simultaneous simulation of iterated Itô integrals for multiple independent Brownian motions, Ann. Appl. Probab., 11 (2001), 470–487. https://doi.org/10.1214/aoap/1015345301
5. Y. Alhojilan, Explicit order $3/2$ Runge-Kutta method for numerical solutions of stochastic differential equations by using Itô-Taylor expansion, Open Math., 17 (2019), 1515–1525. https://doi.org/10.1515/math-2019-0124
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献