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• W3100884045 abstract "We consider stochastic processes on complete, locally compact tree-like metric spaces $(T,r)$ on their “natural scale” with boundedly finite speed measure $nu$. Given a triple $(T,r,nu)$ such a speed-$nu$ motion on $(T,r)$ can be characterized as the unique strong Markov process which if restricted to compact subtrees satisfies for all $x,yin T$ and all positive, bounded measurable $f$, begin{equation}label{eabstract}mathbb{E}^{x}[int^{tau_{y}}_{0}mathrm{d}sf(X_{s})]=2int_{T}nu(mathrm{d}z)r(y,c(x,y,z))f(z)<infty,end{equation} where $c(x,y,z)$ denotes the branch point generated by $x,y,z$. If $(T,r)$ is a discrete tree, $X$ is a continuous time nearest neighbor random walk which jumps from $v$ to $v'sim v$ at rate $frac{1}{2}cdot(nu({v})cdot r(v,v'))^{-1}$. If $(T,r)$ is path-connected, $X$ has continuous paths and equals the $nu$-Brownian motion which was recently constructed in [Trans. Amer. Math. Soc. 365 (2013) 3115–3150]. In this paper, we show that speed-$nu_{n}$ motions on $(T_{n},r_{n})$ converge weakly in path space to the speed-$nu$ motion on $(T,r)$ provided that the underlying triples of metric measure spaces converge in the Gromov–Hausdorff-vague topology introduced in [Stochastic Process. Appl. 126 (2016) 2527–2553]." @default.
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• W3100884045 date "2017-03-01" @default.
• W3100884045 modified "2023-10-18" @default.
• W3100884045 title "Invariance principle for variable speed random walks on trees" @default.
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• W3100884045 doi "https://doi.org/10.1214/15-aop1071" @default.
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