Self-similarity of Brownian motion and a large deviation principle for random fields on a binary tree

1994 ◽  
Vol 98 (1) ◽  
pp. 7-20 ◽  
Author(s):  
Nina Gantert
Keyword(s):  
Brownian Motion ◽  
Random Fields ◽  
Binary Tree ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Self Similarity ◽  
Deviation Principle

scholarly journals LARGE DEVIATIONS FOR FLOWS OF INTERACTING BROWNIAN MOTIONS

2010 ◽  
Vol 10 (03) ◽  
pp. 315-339 ◽  
Author(s):  
A. A. DOROGOVTSEV ◽  
O. V. OSTAPENKO
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stochastic Flows ◽  
Brownian Motions ◽  
Deviation Principle ◽  
And Brownian Motion

We establish the large deviation principle (LDP) for stochastic flows of interacting Brownian motions. In particular, we consider smoothly correlated flows, coalescing flows and Brownian motion stopped at a hitting moment.

An invariance principle and a large deviation principle for the biased random walk on

2020 ◽  
Vol 57 (1) ◽  
pp. 295-313
Author(s):  
Yuelin Liu ◽  
Vladas Sidoravicius ◽  
Longmin Wang ◽  
Kainan Xiang
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Invariance Principle ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Scaling Limit ◽  
Rate Function ◽  
Deviation Principle ◽  
Biased Random Walk

AbstractWe establish an invariance principle and a large deviation principle for a biased random walk ${\text{RW}}_\lambda$ with $\lambda\in [0,1)$ on $\mathbb{Z}^d$ . The scaling limit in the invariance principle is not a d-dimensional Brownian motion. For the large deviation principle, its rate function is different from that of a drifted random walk, as may be expected, though the reflected biased random walk evolves like the drifted random walk in the interior of the first quadrant and almost surely visits coordinate planes finitely many times.

ON A SUFFICIENT CONDITION FOR LARGE DEVIATIONS OF ADDITIVE FUNCTIONALS

2011 ◽  
Vol 11 (01) ◽  
pp. 157-181 ◽  
Author(s):  
KANEHARU TSUCHIDA
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Markov Processes ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stable Processes ◽  
Sufficient Condition ◽  
Additive Functionals ◽  
Deviation Principle ◽  
Symmetric Markov Processes

We prove the large deviation principle for continuous additive functionals under certain assumptions. The underlying symmetric Markov processes include Brownian motion and symmetric and relativistic α-stable processes.

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