The probability distribution of the area bounded by a~Gaussian random contour
Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 2, pp. 357-363
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Let $\rho_i=(\rho_i^1,\rho_i^2)$, $i=1,\dots,N$, be two-dimensional Gaussian random variables with $\mathbf M\rho_i=(r\cos\varphi_i,r\sin\varphi_i)$, $\operatorname{cov}(\rho_i^\alpha,\rho_i^\beta)=\delta_{\alpha\beta}\biggl(4r^2\sin^2\frac{\varphi_i-\varphi_j}2\biggr)$, where $r$ is constant, $0\le\varphi_1\dots\varphi_N2\pi$, and $g$ is a real function. Let $S_N$ be the area bounded by the broken line passing through the points $\rho_1,\dots,\rho_N$. In the paper, the distribution of $S=\lim\limits_{N\to\infty}S_N$ is studied.
@article{TVP_1969_14_2_a18,
author = {V. I. Klyatskin and V. I. Tatarskii},
title = {The probability distribution of the area bounded by {a~Gaussian} random contour},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {357--363},
publisher = {mathdoc},
volume = {14},
number = {2},
year = {1969},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_2_a18/}
}
TY - JOUR AU - V. I. Klyatskin AU - V. I. Tatarskii TI - The probability distribution of the area bounded by a~Gaussian random contour JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1969 SP - 357 EP - 363 VL - 14 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_1969_14_2_a18/ LA - ru ID - TVP_1969_14_2_a18 ER -
V. I. Klyatskin; V. I. Tatarskii. The probability distribution of the area bounded by a~Gaussian random contour. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 2, pp. 357-363. http://geodesic.mathdoc.fr/item/TVP_1969_14_2_a18/