caa a22 4500 475839471 CHVBK 20180406123857.0 cr unu---uuuuu 170329e20000701xx s 000 0 eng 10.1023/A:1006495115904 doi (NATIONALLICENCE)springer-10.1023/A:1006495115904 Almost Sure Convergence of the Numerical Discretization of Stochastic Jump Diffusions [Elektronische Daten] [C. Li, X. Liu] Based on the shuffle product expansion of exponential Lie series in terms of a Philip Hall basis for the stochastic differential equations of jump-diffusion type, we can establish Stratonovich-Taylor-Hall (STH) schemes. However, the STHr scheme converges only at order r in the mean-square sense. In order to have the almost sure Stratonovich-Taylor-Hall (ASTH) schemes, we have to include all the terms related to multiple Poissonian integrals as the moments of multiple Poissonian integrals always have lower orders of magnitudes as compared with those of multiple Brownian integrals. Kluwer Academic Publishers, 2000 jump diffusion nationallicence Stratonovich-Taylor expansion nationallicence exponential Lie series nationallicence Philip Hall basis nationallicence shuffle product nationallicence almost sure convergence nationallicence Li C. Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong aut Liu X. Institute of Applied Mathematics, Academia Sinica, 100080, Beijing, P.R. China aut Acta Applicandae Mathematica Kluwer Academic Publishers 62/3(2000-07-01), 225-244 0167-8019 62:3<225 2000 62 10440 https://doi.org/10.1023/A:1006495115904 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1006495115904 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Li C. Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong aut NATIONALLICENCE 700 1- Liu X. Institute of Applied Mathematics, Academia Sinica, 100080, Beijing, P.R. China aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 62/3(2000-07-01), 225-244 0167-8019 62:3<225 2000 62 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer