Asymptotic behavior of constrained stochastic approximations via the theory of large deviations

1987 ◽  
Vol 75 (2) ◽  
pp. 223-244 ◽  
Author(s):  
Paul Dupuis ◽  
Harold J. Kushner
Keyword(s):  
Asymptotic Behavior ◽  
Large Deviations ◽  
Stochastic Approximations

scholarly journals Precise Large Deviations for Random Sums of END Random Variables with Dominated Variation

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Yu Chen ◽  
Zhihui Qu
Keyword(s):  
Asymptotic Behavior ◽  
Large Deviations ◽  
Risk Model ◽  
Random Variables ◽  
Random Sums ◽  
Tail Probabilities ◽  
Precise Large Deviations ◽  
Surplus Process ◽  
End Random Variables ◽  
Renewal Risk

We investigate the precise large deviations for random sums of extended negatively dependent random variables with long and dominatedly varying tails. We find out that the asymptotic behavior of precise large deviations of random sums is insensitive to the extended negative dependence. We apply the results to a generalized dependent compound renewal risk model including premium process and claim process and obtain the asymptotic behavior of the tail probabilities of the claim surplus process.

scholarly journals Large deviations of the limiting distribution in the Shanks–Rényi prime number race

2012 ◽  
Vol 153 (1) ◽  
pp. 147-166 ◽  
Author(s):  
YOUNESS LAMZOURI
Keyword(s):  
Asymptotic Behavior ◽  
Large Deviations ◽  
Prime Number ◽  
Riemann Hypothesis ◽  
Linear Independence ◽  
Limiting Distribution ◽  
Absolutely Continuous ◽  
Independence Hypothesis ◽  
Vector Valued Function ◽  
Vector Valued

AbstractLet q ≥ 3, 2 ≤ r ≤ φ(q) and a1, . . ., ar be distinct residue classes modulo q that are relatively prime to q. Assuming the Generalized Riemann Hypothesis (GRH) and the Linear Independence Hypothesis (LI), M. Rubinstein and P. Sarnak [11] showed that the vector-valued function Eq;a1, . . ., ar(x) = (E(x;q,a1), . . ., E(x;q,ar)), where $E(x;q,a)= ({\log x}/{\sqrt{x}})(\phi(q)\pi(x;q,a)-\pi(x))$, has a limiting distribution μq;a1, . . ., ar which is absolutely continuous on $\mathbb{R}^r$. Furthermore, they proved that for r fixed, μq;a1, . . ., ar tends to a multidimensional Gaussian as q → ∞. In the present paper, we determine the exact rate of this convergence, and investigate the asymptotic behavior of the large deviations of μq;a1, . . ., ar.

scholarly journals Asymptotic Bahavior of the Moran Particle System

2013 ◽  
Vol 45 (2) ◽  
pp. 379-397
Author(s):  
Shui Feng ◽  
Jie Xiong
Keyword(s):  
Asymptotic Behavior ◽  
Large Deviations ◽  
Random Sampling ◽  
Limit Theorems ◽  
Empirical Process ◽  
Particle System ◽  
Sampling Rate ◽  
Interacting Particle ◽  
Independent Motion ◽  
Number Of Particles

The asymptotic behavior is studied for an interacting particle system that involves independent motion and random sampling. For a fixed sampling rate, the empirical process of the particle system converges to the Fleming-Viot process when the number of particles approaches ∞. If the sampling rate approaches 0 as the number of particles becomes large, the corresponding empirical process will converge to the deterministic flow of the motion. In the main results of this paper, we study the corresponding central limit theorems and large deviations. Both the Gaussian limits and the large deviations depend on the sampling scales explicitly.

Sign in / Sign up

Export Citation Format

Share Document