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Almost Sure Convergence of the Numerical Discretization of Stochastic Jump Diffusions (2000)

Li, C. W. ; Liu, X. Q.

Springer

Acta applicandae mathematicae 62 (2000), S. 225-244

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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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Evidence concerning the morphogenesis of saccular receptors in the bullfrog (Rana catesbeiana)Research sponsored by the Joint Services Electronics Program, Contract F44620-71-C-0087 and the United States Public Health Service, National Institute of Health, grant GM-17523-02. (1973)

Lewis, E. R. ; Li, C. W.

New York, NY : Wiley-Blackwell

Journal of Morphology 139 (1973), S. 351-361

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ISSN: 0362-2525

Keywords: Life and Medical Sciences ; Cell & Developmental Biology

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Biology , Medicine

Notes: A dichotomy of hair-cell types has been found in the bullfrog sacculus, and considerable evidence supports the view that one type (“peripheral”) is transformed during macular growth to the other type (“central”). Between the periphery and the center of the macula, one finds a gradation of form from “peripheral” to “central” type. Occasionally in adults and more often in stage-26 tadpoles one finds the presumably younger peripheral type of hair cell occurring well beyond the limits of the macula proper. The apparent morphogenic sequence for saccular hair cells is (1) development of a kinocillum on an endolymphatic epithelial cell, (2) gradual transformation of microvilli into stereocilia, (3) growth of the stereocilia and development of kinociliary bulb, (4) achievement of final size and form.

Additional Material: 15 Ill.