Concentration of the Brownian bridge on Cartan-Hadamard manifolds with pinched negative sectional curvature
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چکیده
We study the rate of concentration of a Brownian bridge in time one around the corresponding geodesical segment on a Cartan-Hadamard manifold with pinched negative sectional curvature, when the distance between the two extremities tends to infinity. This improves on previous results by A. Eberle [7], and one of us [21]. Along the way, we derive a new asymptotic estimate for the logarithmic derivative of the heat kernel on such manifolds, in bounded time and with one space parameter tending to infinity, which can be viewed as a counterpart to Bismut’s asymptotic formula in small time [3].
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تاریخ انتشار 2004