Large deviations in Axiom A endomorphisms

2003 ◽  
Vol 133 (6) ◽  
pp. 1379-1388 ◽  
Author(s):  
Pei-Dong Liu ◽  
Min Qian ◽  
Yang Zhao
Keyword(s):  
Large Deviations ◽  
Large Deviation ◽  
Axiom A ◽  
Space Technique ◽  
Large Deviation Theorem ◽  
Smale Space

By applying a general large-deviation theorem of Kifer and Ruelle's Smale space technique, some large-deviation estimates are proved for Axiom A endomorphisms.

scholarly journals Sharp large deviations for some hyperbolic systems

2013 ◽  
Vol 35 (1) ◽  
pp. 249-273 ◽  
Author(s):  
VESSELIN PETKOV ◽  
LUCHEZAR STOYANOV
Keyword(s):  
Large Deviations ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Hyperbolic Systems ◽  
Axiom A ◽  
Deviation Principle ◽  
Basic Set ◽  
Sharp Large Deviations ◽  
Additional Regularity ◽  
Sharp Large Deviation

AbstractWe prove a sharp large deviation principle concerning intervals shrinking with sub-exponential speed for certain models involving the Poincaré map related to a Markov family for an Axiom A flow restricted to a basic set $\Lambda $ satisfying some additional regularity assumptions.

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.

Large deviations in the supercritical branching process

1993 ◽  
Vol 25 (04) ◽  
pp. 757-772 ◽  
Author(s):  
J. D. Biggins ◽  
N. H. Bingham
Keyword(s):  
Distribution Function ◽  
Large Deviations ◽  
Population Size ◽  
Branching Process ◽  
Large Deviation ◽  
Moment Generating Function ◽  
Large Deviation Theory ◽  
Tail Behaviour ◽  
The Moment ◽  
Deviation Theory

The tail behaviour of the limit of the normalized population size in the simple supercritical branching process, W, is studied. Most of the results concern those cases when a tail of the distribution function of W decays exponentially quickly. In essence, knowledge of the behaviour of transforms can be combined with some ‘large-deviation' theory to get detailed information on the oscillation of the distribution function of W near zero or at infinity. In particular we show how an old result of Harris (1948) on the asymptotics of the moment-generating function of W translates to tail behaviour.

On the limiting distribution of the failure time of fibrous materials

1983 ◽  
Vol 15 (02) ◽  
pp. 331-348
Author(s):  
Wagner De Souza Borges
Keyword(s):  
Materials Science ◽  
Failure Time ◽  
Large Deviation ◽  
Limiting Distribution ◽  
Statistical Characteristics ◽  
Fibrous Materials ◽  
Large Deviation Theorem ◽  
Science Area ◽  
The Individual ◽  
Failure Time Distributions

A large deviation theorem of the Cramér–Petrov type and a ranking limit theorem of Loève are used to derive an approximation for the statisticaldistribution of the failure time of fibrous materials. For that, fibrousmaterials are modeled as a series of independent and identical bundles of parallel filaments and the asymptotic distribution of their failure time is determined in terms of statistical characteristics of the individual filaments, as both the number of filaments in each bundle and the number of bundles in the chain grow large simultaneously. While keeping the numbernof filaments in each bundle fixed and increasing only the chain lengthkleads to a Weibull limiting distribution for the failure time, letting both increase in such a way that logk(n)= o(n), we show that the limit distribution isfor. Since fibrous materials which are both long and have many filaments prevail, the result is of importance in the materials science area since refined approximations to failure-time distributions can be achieved.

A LARGE DEVIATION FOR OCCUPATION TIME OF SUPER α-STABLE PROCESS

2008 ◽  
Vol 11 (01) ◽  
pp. 53-71 ◽  
Author(s):  
QIU-YUE LI ◽  
YAN-XIA REN
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stable Process ◽  
Rate Function ◽  
Occupation Time ◽  
Occupation Times ◽  
Tail Probabilities ◽  
Super Brownian Motion

We derive a large deviation principle for occupation time of super α-stable process in ℝd with d > 2α. The decay of tail probabilities is shown to be exponential and the rate function is characterized. Our result can be considered as a counterpart of Lee's work on large deviations for occupation times of super-Brownian motion in ℝd for dimension d > 4 (see Ref. 10).

A large deviations heuristic made precise

2000 ◽  
Vol 128 (3) ◽  
pp. 561-569 ◽  
Author(s):  
NEIL O'CONNELL
Keyword(s):  
Large Deviations ◽  
Bin Packing ◽  
Symmetric Functions ◽  
Large Deviation ◽  
Random Variables ◽  
Packing Problem ◽  
Rate Function ◽  
Empirical Measures ◽  
Underlying Distribution ◽  
Uniformly Lipschitz

Sanov's Theorem states that the sequence of empirical measures associated with a sequence of i.d.d. random variables satisfies the large deviation principle (LDP) in the weak topology with rate function given by a relative entropy. We present a derivative which allows one to establish LDPs for symmetric functions of many i.d.d. random variables under the condition that (i) a law of large numbers holds whatever the underlying distribution and (ii) the functions are uniformly Lipschitz. The heuristic (of the title) is that the LDP follows from (i) provided the functions are ‘sufficiently smooth’. As an application, we obtain large deviations results for the stochastic bin-packing problem.

scholarly journals Large Deviations for Stochastic Differential Equations on Sd Associated with the Critical Sobolev Brownian Vector Fields

2011 ◽  
Vol 2011 ◽  
pp. 1-19
Author(s):  
Qinghua Wang
Keyword(s):  
Differential Equations ◽  
Large Deviations ◽  
Stochastic Differential Equations ◽  
Vector Fields ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Deviation Principle

We obtain a large deviation principle for the stochastic differential equations on the sphere Sd associated with the critical Sobolev Brownian vector fields.

Symmetry characterizations of certain distributions, 2: Discounted additive functionals and large deviations

1992 ◽  
Vol 112 (3) ◽  
pp. 599-611 ◽  
Author(s):  
Martin Baxter ◽  
David Williams
Keyword(s):  
Large Deviations ◽  
Financial Markets ◽  
Large Deviation ◽  
Control Problems ◽  
Exact Results ◽  
Focus Attention ◽  
Average Case ◽  
Additive Functionals ◽  
Decision Control ◽  
New Treatment

This paper may be read independently of Baxter and Williams [1], hereinafter denoted by [BW1].As in [BW1], we are mainly concerned with discounted additive functionals. We find that the large-deviation behaviour of the average depends on the precise average used. We derive, in certain cases, a link (but not equality) between the Cesàro average and Abel average limits, and would expect that other averages would produce other limiting behaviours. We have focused on the exponentially discounted (Abel average) case, both because of its tractability and because of its frequent appearance in decision/control problems and models of financial markets. We do give in subsection (e) the promised ‘excursion’ treatment of symmetry characterizations of the type announced in [BW1]; and this new treatment is simpler, more illuminating and more general. First, however, we focus attention on a different kind of asymptotic behaviour from that studied in [BW1], and on differential equations for exact results.

scholarly journals Large deviations for multidimensional state-dependent shot-noise processes

2015 ◽  
Vol 52 (04) ◽  
pp. 1097-1114 ◽  
Author(s):  
Amarjit Budhiraja ◽  
Pierre Nyquist
Keyword(s):  
Large Deviations ◽  
Shot Noise ◽  
Large Deviation ◽  
Physical Systems ◽  
Sample Paths ◽  
State Dependent ◽  
Light Tails ◽  
Engineering Sciences ◽  
Weak Convergence Approach ◽  
Poisson Shot Noise

Shot-noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory, and in the engineering sciences. In this paper we prove a large deviation principle for the sample-paths of a general class of multidimensional state-dependent Poisson shot-noise processes. The result covers previously known large deviation results for one-dimensional state-independent shot-noise processes with light tails. We use the weak convergence approach to large deviations, which reduces the proof to establishing the appropriate convergence of certain controlled versions of the original processes together with relevant results on existence and uniqueness.

Sign in / Sign up

Export Citation Format

Share Document