Levy's stochastic area formula in higher dimensions |
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Authors: | K Helmes A Schwane |
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Institution: | Institut für Angewandte Mathematik, Universität Bonn, Wegelerstrasse 6, D-5300 Bonn, West Germany |
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Abstract: | Let (Wt) = (W1t,W2t,…,Wdt), d ? 2, be a d-dimensional standard Brownian motion and let A(t) be a bounded measurable function from + into the space of d × d skew-symmetric matrices and x(t) such a function into d. A class of stochastic processes (LtA,x), a particular example of which is Levy's “stochastic area” , is dealt with.The joint characteristic function of Wt and L1A,x is calculated and based on this result a formula for fundamental solutions for the hypoelliptic operators which generate the diffusions (Wt,LtA,x) is given. |
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