Almost sure asymptotic behaviour of the -neighbourhood surface area of Brownian paths
Czechoslovak Mathematical Journal (2012)
- Volume: 62, Issue: 1, page 67-75
- ISSN: 0011-4642
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topHonzl, Ondřej, and Rataj, Jan. "Almost sure asymptotic behaviour of the $r$-neighbourhood surface area of Brownian paths." Czechoslovak Mathematical Journal 62.1 (2012): 67-75. <http://eudml.org/doc/246887>.
@article{Honzl2012,
abstract = {We show that whenever the $q$-dimensional Minkowski content of a subset $A\subset \mathbb \{R\}^d$ exists and is finite and positive, then the “S-content” defined analogously as the Minkowski content, but with volume replaced by surface area, exists as well and equals the Minkowski content. As a corollary, we obtain the almost sure asymptotic behaviour of the surface area of the Wiener sausage in $\mathbb \{R\}^d$, $d\ge 3$.},
author = {Honzl, Ondřej, Rataj, Jan},
journal = {Czechoslovak Mathematical Journal},
keywords = {Minkowski content; Kneser function; Brownian motion; Wiener sausage; Minkowski content; Kneser function; Brownian motion; Wiener sausage},
language = {eng},
number = {1},
pages = {67-75},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Almost sure asymptotic behaviour of the $r$-neighbourhood surface area of Brownian paths},
url = {http://eudml.org/doc/246887},
volume = {62},
year = {2012},
}
TY - JOUR
AU - Honzl, Ondřej
AU - Rataj, Jan
TI - Almost sure asymptotic behaviour of the $r$-neighbourhood surface area of Brownian paths
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 1
SP - 67
EP - 75
AB - We show that whenever the $q$-dimensional Minkowski content of a subset $A\subset \mathbb {R}^d$ exists and is finite and positive, then the “S-content” defined analogously as the Minkowski content, but with volume replaced by surface area, exists as well and equals the Minkowski content. As a corollary, we obtain the almost sure asymptotic behaviour of the surface area of the Wiener sausage in $\mathbb {R}^d$, $d\ge 3$.
LA - eng
KW - Minkowski content; Kneser function; Brownian motion; Wiener sausage; Minkowski content; Kneser function; Brownian motion; Wiener sausage
UR - http://eudml.org/doc/246887
ER -
References
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