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- W2059016498 abstract "Let $T^varepsilon_k(lambda; t_1,ldots,t_k) = rho(X_{t_1})q^varepsilon(X_{t_2} - X_{t_1}) cdots q^varepsilon(X_{t_k} - X_{t_k - 1}),$ where $X_t$ is a Brownian motion in $mathbb{R}^2, lambda(dx) = rho(x) dx$ and $q^varepsilon$ converges to Dirac's delta function as $varepsilon downarrow 0$. The self-intersection local times of order $k$ are described by a generalized random field $T_k(lambda; t_1,ldots,t_k) = lim_{varepsilondownarrow 0} T^varepsilon_k(lambda; t_1,ldots,t_k), quadtext{for} 0 < t_1 < cdots < t_k.$ The field blows up as $t_i - t_j rightarrow 0$ for some $i neq j$. We show that with a proper choice of the coefficients $B^l_k(varepsilon)$, a generalized random field $mathscr{J}_k(lambda; t_1,ldots,t_k) = lim_{varepsilondownarrow 0}biglbrack T^varepsilon_k(lambda; t_1,ldots,t_k) + sum^{k - 1}_{l = 1}lbrack B^l_k(varepsilon)T^varepsilon_lrbrack(lambda; t_1,ldots,t_k)bigrbrack$ is well defined for all $0 leq t_1 leq cdots leq t_k$ and it coincides with $T_k(lambda; t_1,ldots,t_k)$ for $t_1 < cdots < t_k$." @default.
- W2059016498 created "2016-06-24" @default.
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- W2059016498 date "1988-01-01" @default.
- W2059016498 modified "2023-09-26" @default.
- W2059016498 title "Regularized Self-Intersection Local Times of Planar Brownian Motion" @default.
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- W2059016498 doi "https://doi.org/10.1214/aop/1176991885" @default.
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