ISSN:
1572-9036
Keywords:
jump diffusion
;
Stratonovich–Taylor expansion
;
exponential Lie series
;
Philip Hall basis
;
shuffle product
;
almost sure convergence
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1006495115904
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