Geodesic
A limit theorem for boundary local time of a symmetric reflected diffusion
Teoriâ slučajnyh processov, Tome 22 (2017) no. 1, pp. 41-61.

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Let $X$ be a symmetric diffusion reflecting in a $\mathcal{C}^{3}$-bounded domain $D\subset\mathbb{R}^{d}$, $d\geq 1$, with a $\mathcal{C}^{2}$-bounded and non-degenerate matrix $a$. For $t>0$ and $n,k\in \mathbb{N}$ let $N(n,t)$ be the number of dyadic intervals $I_{n,k}$ of length $2^{-n}$, $k\geq 0$, that contain a time $s\leq t$ s.t. $X(s)\in\partial D$. For a suitable normalizing factor $H(t)$ we prove, extending the one dimensional case, that a.s. for all $t>0$ the entropy functional $N(n,t)/H(2^{-n})$ converges to the boundary local time $L(t)$ as $n\rightarrow\infty$. Applications include boundary value problems in PDE theory, efficient Monte Carlo simulations and Finance.
Keywords: Reflecting symmetric diffusion, Boundary local time, limit theorem, random scenery.
Mots-clés : Monte Carlo 
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Madani Abdelatif Benchérif. A limit theorem for boundary local time of a symmetric reflected diffusion. Teoriâ slučajnyh processov, Tome 22 (2017) no. 1, pp. 41-61. http://geodesic.mathdoc.fr/item/THSP_2017_22_1_a4/

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