Relationship between Stochastic Flows and Connection Forms

نویسنده

  • MISHA NEKLYUDOV
چکیده

The idea of reconstructing of geometry of riemannian manifold M from the Brownian motion on M has been productively explored for a long time (see, for instance, expository article of Pinsky [7] and references therein). In [7] different asymptotics of Brownian motion (mean exit time, distribution of exit time from small ball,...) has been produced and it was shown that it is possible to retrieve geometry of the manifold through the asymptotics in low dimensions (generally less than six). Another possibility to deduce geometry of the manifold is through small time asymptotics of logarithm of transition function of Brownian motion on manifold (see [8]). Indeed, Bismut-type formula (see, for example, Corollary 3.2, p. 264 of [3]) allow us to deduce logarithm of the transition function p : [0, T ]×M ×M → R of the Brownian motion on the manifold. We have

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تاریخ انتشار 2008