Bootstrap random walks

Andrea Collevecchio, Kais Hamza and Meng Shi

Stochastic Processes and their Applications, 2016, vol. 126, issue 6, 1744-1760

Abstract: Consider a one dimensional simple random walk X=(Xn)n≥0. We form a new simple symmetric random walk Y=(Yn)n≥0 by taking sums of products of the increments of X and study the two-dimensional walk (X,Y)=((Xn,Yn))n≥0. We show that it is recurrent and when suitably normalised converges to a two-dimensional Brownian motion with independent components; this independence occurs despite the functional dependence between the pre-limit processes. The process of recycling increments in this way is repeated and a multi-dimensional analog of this limit theorem together with a transience result are obtained. The construction and results are extended to include the case where the increments take values in a finite set (not necessarily {−1,+1}).

Keywords: Random walks; Functional limit theorem (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2015.11.016

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