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Using the first exit time for Brownian motion from a smoothly bounded domain in Euclidean space, we define two natural functionals on the space of embedded, compact, oriented, unparametrized hypersurfaces in Euclidean space. We develop explicit formulas for the first variation of each of the functionals and characterize the critical points.
Gaussian random function is a random function whose values are normally distributed and has some good properties (e.g., Lifshits , Tarpey and Kinateder , Shimizu and Mizuta ). In this presentation, we discuss hypothesis testing for multivariate Gaussian random function. A random function can be viewed as an infinite (p = ∞) dimensional random… (More)