Abstract
Denote by Diff(M) the group of C ∞ diffeomorphisms of a Riemannian manifold M. Define a Brownian flow on M as a Diff(M)-valued process Φt, with independent increments (Φt1, Φt2 ο Φt1 -1, ..., Φt1+1 ο Φti -1 if, t1 < t2 ... < ti). We assume in addition that the increments of the flow are stationary (Φs(law) ~ Φt+s ο Φt -1) and that for any init ial value x ∈ M, the one point process Φt(x) is a Brownian motion on M. An analytical characterization of Brownian flows is given in [1].
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le Jan, Y. (1991). Asymptotic Properties of Isotropic Brownian Flows. In: Alexander, K.S., Watkins, J.C. (eds) Spatial Stochastic Processes. Progress in Probability, vol 19. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0451-0_10
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DOI: https://doi.org/10.1007/978-1-4612-0451-0_10
Publisher Name: Birkhäuser, Boston, MA
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