Projects per year
Abstract
Consider a one dimensional simple random walk X = (X_{n})_{n≥0}. We form a new simple symmetric random walk Y = (Y_{n})_{n≥0} by taking sums of products of the increments of X and study the twodimensional walk (X,Y) = ((X_{n}, Y_{n}))_{n≥0}. We show that it is recurrent and when suitably normalised converges to a twodimensional Brownian motion with independent components; this independence occurs despite the functional dependence between the prelimit processes. The process of recycling increments in this way is repeated and a multidimensional 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}).
Original language  English 

Pages (fromto)  17441760 
Number of pages  17 
Journal  Stochastic Processes and their Applications 
Volume  126 
Issue number  6 
DOIs  
Publication status  Published  1 Jun 2016 
Keywords
 Functional limit theorem
 Random walks
Projects
 1 Finished

Finite Markov chains in statistical mechanics and combinatorics
Garoni, T., Collevecchio, A. & Markowsky, G.
Australian Research Council (ARC)
2/01/14 → 31/12/17
Project: Research