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On minimal parabolic functions and time-homogenous parabolic h-transforms
(American Mathematical Society, 1999-03-29)
Does a minimal harmonic function h remain minimal when it is viewed as a parabolic function? The question is answered for a class of long thin semi-infinite tubes D [is an element of the subset of real numbers to the power of] d of variable width and minimal harmonic functions h corresponding to the boundary point of D "at ...
Stochastic bifurcation models
(Institute of Mathematical Statistics, 1999-01)
We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray-Knight theorems), and on time and direction of bifurcation. A relationship with Lipschitz approximations to Brownian paths is also discussed.