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An Almost Sure Invariance Principle for Renormalized Intersection Local Times

   
@article{EJP236,
	author = {Richard Bass and Jay Rosen},
	title = {An Almost Sure Invariance Principle for Renormalized Intersection Local Times},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {10},
	year = {2005},
	keywords = {},
	abstract = {Let $\beta_k(n)$ be the number of self-intersections of order $k$, appropriately renormalized, for a mean zero planar random walk with $2+\delta$ moments. On a suitable probability space we can construct the random walk and a planar Brownian motion $W_t$ such that for each $k \geq 2$, $|\beta_k(n)- \gamma_k(n)|=o(1)$, a.s., where $\gamma_k(n)$ is the renormalized self-intersection local time of order $k$ at time 1 for the Brownian motion $W_{nt}/\sqrt n$.},
	pages = {no. 4, 124-164},
	issn = {1083-6489},
	doi = {10.1214/EJP.v10-236},    
        url = {http://ejp.ejpecp.org/article/view/236}}