Brownian motion and a sharply curved boundary
- 1 March 1981
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 13 (04) , 736-750
- https://doi.org/10.1017/s000186780003648x
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) – N 1/2 c(t)}, where c is a smooth function with a unique minimum of 0 at t = 1, and he derived an approximation to this distribution which he showed to be accurate to order N –1/4. In this paper, his approximation is shown to be accurate to order N –1/3, and a refined approximation is given which is accurate to order N –1/2 log N. 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 3 references indexed in Scilit:
- An approximation of partial sums of independent RV'-s, and the sample DF. IProbability Theory and Related Fields, 1975
- The maximum size of a closed epidemicAdvances in Applied Probability, 1974
- The Asymptotic Analysis of a Stochastic Model of an EpidemicTheory of Probability and Its Applications, 1970