Brownian Occupation Measures on Compact Manifolds

  • Gunnar A. Brosamler
Part of the Progress in Probability and Statistics book series (PRPR, volume 12)


Let M be a compact C manifold of dimension d. A C metric g and a C vector field V on M determine a “Brownian motion” on M, i.e. a strong Markov process with continuous sample paths and generator \( L = \frac{1}{{2\,}} {\Delta_g} + V, \) where Δ g stands for the Laplace-Beltrami operator, associated with g. (If necessary we indicate by the subscript g, that an object is associated with the metric g.) Notice that the metric and the vector field can be recovered from the Brownian motion, from its generator L, to be precise.


Brownian Motion Iterate Logarithm Invariant Probability Measure Vector Field Versus Strong Markov Process 


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Copyright information

© Birkhäuser Boston, Inc. 1986

Authors and Affiliations

  • Gunnar A. Brosamler
    • 1
    • 2
  1. 1.Fachbereich MathematikUniversitaet des SaarlandesSaarbrueckenWest Germany
  2. 2.Department of MathematicsThe University of British ColumbiaVancouverCanada

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