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A Stochastic Two-Point Boundary Value Problem
Electronic Journal of Probability
We investigate the two-point stochastic boundary-value problem on [0, 1]: whereẆ is a white noise on [0, 1], ξ and η are random variables, and f and g are continuous real-valued functions. This is the stochastic analogue of the deterministic two point boundary-value problem, which is a classical example of bifurcation. We find that if f and g are affine, there is no bifurcation: for any r.v. ξ and η, (0) has a unique solution a.s. However, as soon as f is non-linear, bifurcation appears. Wedoi:10.1214/ejp.v7-111 fatcat:mok25ej6gfhipf5lk5vngpnjia