scholarly journals Higher order asymptotics for large deviations – Part I

2020 ◽  
pp. 1-39 ◽  
Author(s):  
Kasun Fernando ◽  
Pratima Hebbar
Keyword(s):  
Large Deviations ◽  
Higher Order ◽  
Higher Order Asymptotics

scholarly journals Higher-order asymptotics and critical indexes in the ϕ3 theory

2014 ◽  
Vol 884 ◽  
pp. 672-683 ◽  
Author(s):  
G.A. Kalagov ◽  
M.Yu. Nalimov
Keyword(s):  
Higher Order ◽  
Higher Order Asymptotics

Large deviations and the Bayesian estimation of higher-order Markov transition functions

1996 ◽  
Vol 33 (1) ◽  
pp. 18-27 ◽  
Author(s):  
F. Papangelou
Keyword(s):  
Large Deviations ◽  
Bayesian Estimation ◽  
Transition Function ◽  
Higher Order ◽  
Positive Probability ◽  
State Spaces ◽  
Empirical Distributions ◽  
Transition Functions ◽  
Markov Transition ◽  
Finite State

In the Bayesian estimation of higher-order Markov transition functions on finite state spaces, a prior distribution may assign positive probability to arbitrarily high orders. If there are n observations available, we show (for natural priors) that, with probability one, as n → ∞ the Bayesian posterior distribution ‘discriminates accurately' for orders up to β log n, if β is smaller than an explicitly determined β0. This means that the ‘large deviations' of the posterior are controlled by the relative entropies of the true transition function with respect to all others, much as the large deviations of the empirical distributions are governed by their relative entropies with respect to the true transition function. An example shows that the result can fail even for orders β log n if β is large.

scholarly journals Higher order asymptotics for large deviations — Part II

2020 ◽  
pp. 2150025
Author(s):  
Kasun Fernando ◽  
Pratima Hebbar
Keyword(s):  
Large Deviations ◽  
Asymptotic Expansions ◽  
Continuous Time ◽  
Compact Manifold ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Hörmander Condition ◽  
Additive Functionals ◽  
Higher Order Asymptotics ◽  
Weakly Dependent

We obtain asymptotic expansions for the large deviation principle (LDP) for continuous time stochastic processes with weakly-dependent increments. As a key example, we show that additive functionals of solutions of stochastic differential equations (SDEs) satisfying Hörmander condition on a [Formula: see text]-dimensional compact manifold admit these asymptotic expansions of all orders.

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