scholarly journals On the Lower Bound of Large Deviation of Random Walks

1985 ◽  
Vol 13 (1) ◽  
pp. 90-96 ◽  
Author(s):  
Tzuu-Shuh Chiang
Keyword(s):  
Lower Bound ◽  
Random Walks ◽  
Large Deviation

scholarly journals Convex hulls of multiple random walks: A large-deviation study

2016 ◽  
Vol 94 (5) ◽  
Author(s):  
Timo Dewenter ◽  
Gunnar Claussen ◽  
Alexander K. Hartmann ◽  
Satya N. Majumdar
Keyword(s):  
Random Walks ◽  
Large Deviation ◽  
Convex Hulls

scholarly journals Convex hulls of random walks: Large-deviation properties

2015 ◽  
Vol 91 (5) ◽  
Author(s):  
Gunnar Claussen ◽  
Alexander K. Hartmann ◽  
Satya N. Majumdar
Keyword(s):  
Random Walks ◽  
Large Deviation ◽  
Convex Hulls

LARGE DEVIATION ASYMPTOTICS FOR RANDOM-WALK TYPE PERTURBATIONS

2007 ◽  
Vol 07 (01) ◽  
pp. 75-89
Author(s):  
ZHIHUI YANG
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
White Noise ◽  
Wiener Process ◽  
Stochastic Resonance ◽  
Large Deviation ◽  
Correction Term ◽  
Exit Problem ◽  
Wiener Processes ◽  
Noise Type

Symmetric random walks can be arranged to converge to a Wiener process in the area of normal deviation. However, random walks and Wiener processes have, in general, different asymptotics of the large deviation probabilities. The action functionals for random-walks and Wiener processes are compared in this paper. The correction term is calculated. Exit problem and stochastic resonance for random-walk-type perturbation are also considered and compared with the white-noise-type perturbation.

Embedding submartingales in wiener processes with drift, with applications to sequential analysis

1969 ◽  
Vol 6 (03) ◽  
pp. 612-632 ◽  
Author(s):  
W. J. Hall
Keyword(s):  
Lower Bound ◽  
Random Walks ◽  
Sample Size ◽  
Wiener Process ◽  
Likelihood Ratio ◽  
Sequential Analysis ◽  
Stopping Times ◽  
Wiener Processes ◽  
Size Function ◽  
Log Likelihood

Summary Skorokhod (1961) demonstrated how the study of martingale sequences (and zero-mean random walks) can be reduced to the study of the Wiener process (without drift) at a sequence of random stopping times. We show how the study of certain submartingale sequences, including certain random walks with drift and log likelihood ratio sequences, can be reduced to the study of the Wiener process with drift at a sequence of stopping times (Theorem 4.1). Applications to absorption problems are given. Specifically, we present new derivations of a number of the basic approximations and inequalities of classical sequential analysis, and some variations on them — including an improvement on Wald's lower bound for the expected sample size function (Corollary 7.5).

scholarly journals Deviation bounds for the first passage time in the frog model

2019 ◽  
Vol 51 (01) ◽  
pp. 184-208 ◽  
Author(s):  
Naoki Kubota
Keyword(s):  
Random Walks ◽  
Large Deviation ◽  
First Passage Time ◽  
Passage Time ◽  
The Other ◽  
Active Particle ◽  
First Passage ◽  
Cubic Lattice ◽  
Concentration Bounds ◽  
Frog Model

AbstractWe consider the so-called frog model with random initial configurations. The dynamics of this model are described as follows. Some particles are randomly assigned to any site of the multidimensional cubic lattice. Initially, only particles at the origin are active and these independently perform simple random walks. The other particles are sleeping and do not move at first. When sleeping particles are hit by an active particle, they become active and start moving in a similar fashion. The aim of this paper is to derive large deviation and concentration bounds for the first passage time at which an active particle reaches a target site.

scholarly journals Monotonicity of Avoidance Coupling on KN

2016 ◽  
Vol 26 (1) ◽  
pp. 16-23 ◽  
Author(s):  
OHAD N. FELDHEIM
Keyword(s):  
Lower Bound ◽  
Random Walks ◽  
Complete Graph ◽  
Partially Ordered ◽  
Monotonicity Result

Answering a question by Angel, Holroyd, Martin, Wilson and Winkler [1], we show that the maximal number of non-colliding coupled simple random walks on the complete graph KN, which take turns, moving one at a time, is monotone in N. We use this fact to couple [N/4] such walks on KN, improving the previous Ω(N/log N) lower bound of Angel et al. We also introduce a new generalization of simple avoidance coupling which we call partially ordered simple avoidance coupling, and provide a monotonicity result for this extension as well.

scholarly journals DYNAMIC QUANTUM BERNOULLI RANDOM WALKS

2008 ◽  
Vol 11 (02) ◽  
pp. 213-229
Author(s):  
NADINE GUILLOTIN-PLANTARD ◽  
RENÉ SCHOTT
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Random Walks ◽  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Large Numbers

Quantum Bernoulli random walks can be realized as random walks on the dual of SU(2). We use this realization in order to study a model of dynamic quantum Bernoulli random walk with time-dependent transitions. For the corresponding dynamic random walk on the dual of SU(2), we prove several limit theorems (local limit theorem, central limit theorem, law of large numbers, large deviation principle). In addition, we characterize a large class of transient dynamic random walks.

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