Almost sure asymptotic behaviour of the $r$-neighbourhood surface area of Brownian paths
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 67-75.

Voir la notice de l'article dans Czech Digital Mathematics Library

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 $\mathbb R^d$, $d\geq 3$.
DOI : 10.1007/s10587-012-0017-6
Classification : 28A75, 52A20, 52A38, 60D05, 60J65
Mots-clés : Minkowski content; Kneser function; Brownian motion; Wiener sausage 
@article{10_1007_s10587_012_0017_6,
     author = {Honzl, Ond\v{r}ej and Rataj, Jan},
     title = {Almost sure asymptotic behaviour of the $r$-neighbourhood surface area of {Brownian} paths},
     journal = {Czechoslovak Mathematical Journal},
     pages = {67--75},
     publisher = {mathdoc},
     volume = {62},
     number = {1},
     year = {2012},
     doi = {10.1007/s10587-012-0017-6},
     mrnumber = {2899735},
     zbl = {1249.28003},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0017-6/}
}
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
SP  - 67
EP  - 75
VL  - 62
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0017-6/
DO  - 10.1007/s10587-012-0017-6
LA  - en
ID  - 10_1007_s10587_012_0017_6
ER  - 
%0 Journal Article
%A Honzl, Ondřej
%A Rataj, Jan
%T Almost sure asymptotic behaviour of the $r$-neighbourhood surface area of Brownian paths
%J Czechoslovak Mathematical Journal
%D 2012
%P 67-75
%V 62
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0017-6/
%R 10.1007/s10587-012-0017-6
%G en
%F 10_1007_s10587_012_0017_6
Honzl, Ondřej; Rataj, Jan. Almost sure asymptotic behaviour of the $r$-neighbourhood surface area of Brownian paths. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 67-75. doi : 10.1007/s10587-012-0017-6. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0017-6/

Cité par Sources :