Brownian motion and a sharply curved boundary
- 1 December 1981
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 13 (4) , 736-750
- https://doi.org/10.2307/1426970
Abstract
Daniels (1974) reduced the problem of approximating the distribution of the maximum size of a closed epidemic to that of finding the distribution of max0≦t≦2{W(t) –N1/2c(t)}, wherecis a smooth function with a unique minimum of 0 att= 1, and he derived an approximation to this distribution which he showed to be accurate to orderN–1/4. In this paper, his approximation is shown to be accurate to orderN–1/3, and a refined approximation is given which is accurate to orderN–1/2logN.The new approximation is still normal, and its accuracy is similar to that of the original approximation of a discrete process by the Wiener process.Keywords
This publication has 4 references indexed in Scilit:
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