Heat kernel, eigenfunctions, and conditioned Brownian motion in planar domains

Conditioned Brownian motion in planar domains

We give an upper bound for the Green functions of conditioned Brownian motion in planar domains. A corollary is the conditional gauge theorem in bounded planar domains. Short title: Conditioned Brownian motion AMS Subject Classification (1985): Primary 60J50; Secondary 60J45, 60J65

Heat Equation and Reflected Brownian Motion in Time Dependent Domains

Heat Kernel Smoothing Using Laplace-Beltrami Eigenfunctions

We present a novel surface smoothing framework using the Laplace-Beltrami eigenfunctions. The Green's function of an isotropic diffusion equation on a manifold is constructed as a linear combination of the Laplace-Beltraimi operator. The Green's function is then used in constructing heat kernel smoothing. Unlike many previous approaches, diffusion is analytically represented as a series expansi...

Expected lifetime of h-conditioned Brownian motion

Let τΩ denote the lifetime of Brownian motion in a domain Ω ⊂ R. We obtain the asymptotic behaviour of its expected lifetime E x [τΩ] as y → x, where the Brownian motion is conditioned to start at x and to exit at y. 2000 Mathematics Subject Classification: 60J65, 58J35, 35K20.

Integrated Brownian Motion, Conditioned to Be Positive

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