Random Probability Measures on Polish Spaces

By H. Crauel. 2002

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Accuracy of simulations for stochastic dynamic models (2005, methodology): “Q.E.D. Finally, we present a simplified version of Crauel (2002), Proposition 6.21, page 95.”
Stochastic climate dynamics: Random attractors and time-dependent invariant measures (2011, methodology): “The inverse operation of μ 7→ ρ = E[μ•] is then given by ρ 7→ μω = limt→∞ Φ(−t, ω)−1ρ; the latter is in fact the pullback limit of ρ due to the cocycle property [25].”
The correlated pseudomarginal method (2015, methodology): “Crauel, H. (2003) Random Probability Measures on Polish Spaces.”
Asymptotic compactness and absorbing sets for 2D stochastic Navier-Stokes equations on some unbounded domains (2006, background): “From now on, let X be the σ -ﬁeld on C generated by open sets with respect to the Hausdorﬀ metric ρ ; e.g. [8], [15] or Crauel [16].”
On the structure of attractors and invariant measures for a class of monotone random systems (2004, unknown): “By definition (see, e.g. Arnold 1998: chapter 1 or Crauel 2002), a probability measure on ð X;F BðXÞÞ is an ’invariant measure’ for the RDS (#, ’) iff ð X f ð!”