scholarly journals A Note on the Large Deviation Principle for Discrete Associated Random Variables

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Przemysław Matuła ◽  
Maciej Ziemba
Keyword(s):  
Large Deviation Principle ◽  
Large Deviation ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stationary Sequence ◽  
Arithmetic Means ◽  
Associated Random Variables ◽  
Partial Sum ◽  
Deviation Principle ◽  
Uniformly Bounded

We present sufficient conditions under which the sequence of arithmetic means Sn/n, where Sn=X1+⋯+Xn, is the partial sum built on a stationary sequence {Xn}n≥1 of associated integer-valued and uniformly bounded random variables, which satisfy the large deviation principle.

scholarly journals On asymptotically efficient simulation of large deviation probabilities

2005 ◽  
Vol 37 (2) ◽  
pp. 539-552 ◽  
Author(s):  
A. B. Dieker ◽  
M. Mandjes
Keyword(s):  
Importance Sampling ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Sufficient Conditions ◽  
Sampling Distribution ◽  
Efficient Simulation ◽  
Deviation Principle ◽  
Asymptotically Efficient Estimator ◽  
Asymptotically Efficient ◽  
Necessary And Sufficient

Let {νε, ε>0} be a family of probabilities for which the decay is governed by a large deviation principle, and consider the simulation of νε0(A) for some fixed measurable set A and some ε0>0. We investigate the circumstances under which an exponentially twisted importance sampling distribution yields an asymptotically efficient estimator. Varadhan's lemma yields necessary and sufficient conditions, and these are shown to improve on certain conditions of Sadowsky. This is illustrated by an example to which Sadowsky's conditions do not apply, yet for which an efficient twist exists.

scholarly journals On asymptotically efficient simulation of large deviation probabilities

2005 ◽  
Vol 37 (02) ◽  
pp. 539-552 ◽  
Author(s):  
A. B. Dieker ◽  
M. Mandjes
Keyword(s):  
Importance Sampling ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Sufficient Conditions ◽  
Sampling Distribution ◽  
Efficient Simulation ◽  
Deviation Principle ◽  
Asymptotically Efficient Estimator ◽  
Asymptotically Efficient ◽  
Necessary And Sufficient

Let {νε, ε>0} be a family of probabilities for which the decay is governed by a large deviation principle, and consider the simulation of νε0(A) for some fixed measurable setAand some ε0>0. We investigate the circumstances under which an exponentially twisted importance sampling distribution yields an asymptotically efficient estimator. Varadhan's lemma yields necessary and sufficient conditions, and these are shown to improve on certain conditions of Sadowsky. This is illustrated by an example to which Sadowsky's conditions do not apply, yet for which an efficient twist exists.

Large deviation principle for the field in prequantum classical statistical field theory

2017 ◽  
Vol 20 (04) ◽  
pp. 1750025
Author(s):  
Andrei Khrennikov ◽  
Achref Majid
Keyword(s):  
Field Theory ◽  
Random Field ◽  
Field Model ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Background Field ◽  
Deviation Principle ◽  
Statistical Field ◽  
Statistical Field Theory

In this paper, we prove a large deviation principle for the background field in prequantum statistical field model. We show a number of examples by choosing a specific random field in our model.

scholarly journals Chover-Type Laws of the Iterated Logarithm for Kesten-Spitzer Random Walks in Random Sceneries Belonging to the Domain of Stable Attraction

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Wensheng Wang ◽  
Anwei Zhu
Keyword(s):  
Random Walk ◽  
Large Deviation ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Domain Of Attraction ◽  
Stable Law ◽  
Iterated Logarithm ◽  
Cluster Set ◽  
Random Scenery ◽  
Unique Integer

Let X={Xi,i≥1} be a sequence of real valued random variables, S0=0 and Sk=∑i=1kXi  (k≥1). Let σ={σ(x),x∈Z} be a sequence of real valued random variables which are independent of X’s. Denote by Kn=∑k=0nσ(⌊Sk⌋)  (n≥0) Kesten-Spitzer random walk in random scenery, where ⌊a⌋ means the unique integer satisfying ⌊a⌋≤a<⌊a⌋+1. It is assumed that σ’s belong to the domain of attraction of a stable law with index 0<β<2. In this paper, by employing conditional argument, we investigate large deviation inequalities, some sufficient conditions for Chover-type laws of the iterated logarithm and the cluster set for random walk in random scenery Kn. The obtained results supplement to some corresponding results in the literature.

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