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From Fourier to Gegenbauer: Dimension walks on spheres
Fourier to Gegenbauer Dimension walks on spheres
2013/4/28
We show that the even- resp. odd-dimensional Schoenberg coefficients in Gegenbauer expansions of isotropic positive definite functions on the d-sphere can be expressed as linear combinations of Fourie...
The Dimension of the Frontier of Planar Brownian Motion
Planar Brownian Motion Frontier Dimension Disconnection Exponents
2009/5/11
Let $B$ be a two dimensional Brownian motion and let the frontier of $B[0,1]$ be defined as the set of all points in $B[0,1]$ that are in the closure of the unbounded connected component of its comple...
Let $B(t)$ be a Brownian motion in $R^3$. A {it subpath} of the Brownian path $B[0,1]$ is a continuous curve $gamma(t)$, where $gamma[0,1] subseteq B[0,1]$ , $gamma(0) = B(0)$, and $gamma(1) = B(1)$. ...
Support of a Marcus equation in Dimension 1
Marcus equation pathwise representation support theorem
2009/5/4
The purpose of this note is to give a support theorem in the Skorohod space for a one-dimensional Marcus differential equation driven by a Lévy process, without any assumption on the latter. We also g...