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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Acta applicandae mathematicae 62 (2000), S. 225-244 
    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
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