Gaussian fluctuation for spatial average of super-Brownian motion

2021/11/16 by Li, Zenghu, Pu, Fei
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2111.08423

Abstract

Let \u(t , x)\_{(t, x)∈ ℝ+× ℝ} be the density of one-dimensional super-Brownian motion starting from Lebesgue measure. Using the Laplace functional of super-Brownian motion, we prove that as N→ ∞, the normalized spatial integral N^-1/2∫₀^xN[u(t , z)-1 ]\rmd z converges jointly in (t, x) to Brownian sheet in distribution.

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