TY - JOUR
T1 - Markov Chains on Graphs and Brownian Motion
AU - Enriquez, Nathanaël
AU - Kifer, Yuri
PY - 2001
Y1 - 2001
N2 - We consider random walks with small fixed steps inside of edges of a graph script G sign, prescribing a natural rule of probabilities of jumps over a vertex. We show that after an appropriate rescaling such random walks weakly converge to the natural Brownian motion on script G sign constructed in Ref. 1.
AB - We consider random walks with small fixed steps inside of edges of a graph script G sign, prescribing a natural rule of probabilities of jumps over a vertex. We show that after an appropriate rescaling such random walks weakly converge to the natural Brownian motion on script G sign constructed in Ref. 1.
KW - Brownian motion on graphs
KW - Invariance principle
KW - Random walks
UR - http://www.scopus.com/inward/record.url?scp=0035611695&partnerID=8YFLogxK
U2 - 10.1023/A:1011119932045
DO - 10.1023/A:1011119932045
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AN - SCOPUS:0035611695
SN - 0894-9840
VL - 14
SP - 495
EP - 510
JO - Journal of Theoretical Probability
JF - Journal of Theoretical Probability
IS - 2
ER -