An Invariance Principle for Brownian Motion in Random Scenery
نویسندگان
چکیده
We prove an invariance principle for Brownian motion in Gaussian or Poissonian random scenery by the method of characteristic functions. Annealed asymptotic limits are derived in all dimensions, with a focus on the case of dimension d = 2, which is the main new contribution of the paper.
منابع مشابه
Random Walks and Brownian Motion
Tags for today's lecture: Donsker's invariance priciple, Stochastic integration, Itô's formula In this lecture we show an application of Donsker's invariance principle and then proceed to the construction of Itô's stochastic integral. We recall the definitions and give a simple example of an application of the invariance principle. Consider a random walk S n = Σ n i=1 x i with E(x) = 0, E(x 2) ...
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