Burdzy, KrzysztofBass, Richard F.2005-11-292005-11-291999-01Bass, R.F. & K. Burdzy. (1999). Stochastic bifurcation models. Annals of Probability, 27(1): 50-108.http://hdl.handle.net/1773/2197We 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.387215 bytesapplication/pdfen-USBrownian motionfractional Brownian motiondifferential equationsstochastic differential equationslocal timeTrotter theoremRay-Knight theoremLipschitz approximationbifurcationbifurcation timeArticle