论文信息 - The Accuracy of Cauchy Approximation for the Windings of Planar Brownian Motion

The Accuracy of Cauchy Approximation for the Windings of Planar Brownian Motion

Our method of proof relies upon the skew–product representation of planar Brownian motion, and changes of probabilities between the laws of Bessel processes, as indicated in [8], [9], [10]; in particular, this paper is an improvement of [10], which discusses only the case k = 2. The spirit of our expansion is close to the Edgeworth type expansions in the central limit theorems, that is, to the asymptotic expansions of the distribution

Gyula Pap | Marc Yor | M. Yor | G. Pap

[1] Frank Spitzer,et al. Some theorems concerning 2-dimensional Brownian motion , 1958 .

[2] William Feller,et al. An Introduction to Probability Theory and Its Applications , 1951 .

[3] V. V. Petrov. Sums of Independent Random Variables , 1975 .

[4] R. Rao,et al. Normal Approximation and Asymptotic Expansions , 1976 .

[5] William Feller,et al. An Introduction to Probability Theory and Its Applications , 1967 .

[6] Werner Wolf,et al. Convergence theorems with a stable limit law , 1993, Mathematical research.

[7] M. Yor,et al. Continuous martingales and Brownian motion , 1990 .

[8] M. Yor,et al. Loi de l'indice du lacet Brownien, et distribution de Hartman-Watson , 1980 .