# Almost sure asymptotic behaviour of the $r$-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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