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- W202897343 abstract "Fix two rectangles A,B in [0,1]2. Then the size of the random set of double points of the Brownian sheet (W t )t∈[0,1]2 in ℝ d , i. e. the set of pairs (s,t),where s ∈ A, t ∈ B, and W s = W t , can be measured as usual by a self-intersection local time. If A = B, we show that the critical dimension below which self-intersection local time exists, is given by d = 4. If A ⋂ B consists of an axial parallel line, it is 6, if it consists of a point or is empty, 8. In all cases, we derive the rate of explosion of canonical approximations of self-intersection local time for dimensions above the critical one, and determine its smoothness in terms of the canonical Dirichlet structure on Wiener space." @default.
- W202897343 created "2016-06-24" @default.
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- W202897343 date "1995-01-01" @default.
- W202897343 modified "2023-09-25" @default.
- W202897343 title "Critical Dimensions for the Existence of Self-Intersection Local Times of the Brownian Sheet in ℝ d" @default.
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- W202897343 doi "https://doi.org/10.1007/978-3-0348-7026-9_11" @default.
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