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2018 Renormalization of local times of super-Brownian motion
Jieliang Hong
Electron. J. Probab. 23: 1-45 (2018). DOI: 10.1214/18-EJP231

Abstract

For the local time $L_t^x$ of super-Brownian motion $X$ starting from $\delta _0$, we study its asymptotic behavior as $x\to 0$. In $d=3$, we find a normalization $\psi (x)=((2\pi ^2)^{-1} \log (1/|x|))^{1/2}$ such that $(L_t^x-(2\pi |x|)^{-1})/\psi (x)$ converges in distribution to standard normal as $x\to 0$. In $d=2$, we show that $L_t^x-\pi ^{-1} \log (1/|x|)$ converges a.s. as $x\to 0$. We also consider general initial conditions and get some renormalization results. The behavior of the local time allows us to derive a second order term in the asymptotic behavior of a related semilinear elliptic equation.

Citation

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Jieliang Hong. "Renormalization of local times of super-Brownian motion." Electron. J. Probab. 23 1 - 45, 2018. https://doi.org/10.1214/18-EJP231

Information

Received: 18 November 2017; Accepted: 4 October 2018; Published: 2018
First available in Project Euclid: 30 October 2018

zbMATH: 06970414
MathSciNet: MR3878134
Digital Object Identifier: 10.1214/18-EJP231

Subjects:
Primary: 35J61, 60J55, 60J68

JOURNAL ARTICLE
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Vol.23 • 2018
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