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Abstract
Firstly, we compute the distribution function for the hitting time of a linear time-dependent boundary t ↦ a + bt, a ≥ 0, b ∈ ℝ, by a reflecting Brownian motion. The main tool hereby is Doob’s formula which gives the probability that Brownian motion started inside a wedge does not hit this wedge. Other key ingredients are the time inversion property of Brownian motion and the time reversal property of diffusion bridges. Secondly, this methodology can also be applied for the three-dimensional Bessel process. Thirdly, we consider Bessel bridges from 0 to 0 with dimension parameter δ > 0 and show that the probability that such a Bessel bridge crosses an affine boundary is equal to the probability that this Bessel bridge stays below some fixed value.
Eberhart, W. and Elbert, Á., On the eigenvalues of a half-linear boundary value problem, Math. Nachr. 213 (2000), 57-76. MR 2001b :34035 On the eigenvalues of a half-linear boundary value problem
constructed to classify 3 different origins of yellow wine samples, which generated non-linear boundaries between classes. Classification accuracy was used to evaluate the performance of the discriminant model and check if there were significant differences
. Cluster analysis of different grade rapeseed oil samples LDA algorithm is a simple technique to generate non-linear boundaries between classes. LDA algorithm attempts to find a linear combination of features that characterizes or separates two or more
