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Local Limit Theorems for Moderate Deviations and Large Deviations
We prove the local limit theorem in the regimes of moderate deviations and large deviations. In these cases the asymptotic behavior of...
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Normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for the SDE
In this paper, we establish normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for SDE. Due to our results,...
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Self-Normalized Cramér-Type Moderate Deviations for Explosive Vasicek Model
By deviation inequalities for multiple Wiener–Itô integrals, we study the deviation inequalities for some quadratic functionals in the explosive...
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Moderate Deviations for Parameter Estimation in the Fractional Ornstein-Uhlenbeck Processes with Periodic Mean
In this paper, we study the asymptotic properties for the drift parameter estimators in the fractional Ornstein-Uhlenbeck process with periodic mean...
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Moderate deviations for fully coupled multiscale weakly interacting particle systems
We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations...
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On the Asymptotic Behavior of Probabilities of Moderate Deviations for Combinatorial Sums
AbstractIn this paper, the asymptotic behavior of probabilities of moderate deviations is investigated for combinatorial sums of independent random...
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Large and Moderate Deviations for Empirical Density Fields of Stochastic Seir Epidemics with Vertex-Dependent Transition Rates
In this paper, we are concerned with stochastic susceptible-exposed-infected-removed epidemics on complete graphs with vertex-dependent transition...
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Uniform Cramér moderate deviations and Berry–Esseen bounds for superadditive bisexual branching processes in random environments
Let ( Z n ) be a superadditive bisexual branching process in an independent and identically distributed (i.i.d.) random environment ξ . We establish...
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Moderate Deviations for Two-Time Scale Systems with Mixed Fractional Brownian Motion
This work focuses on moderate deviations for two-time scale systems with mixed fractional Brownian motion. Our proof uses the weak convergence method...
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Berry-Esseen bounds and moderate deviations for the norm, entries and spectral radius of products of positive random matrices
Let ( g n ) n ⩾l be a sequence of independent and identically distributed positive random d × d matrices and consider the matrix product G n = g n ⋯ g 1 ....
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Moderate deviations for systems of slow–fast stochastic reaction–diffusion equations
The goal of this paper is to study the moderate deviation principle for a system of stochastic reaction–diffusion equations with a time-scale...
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Limit Theorem for the Moment of Maximum of a Random Walk Reaching a Fixed Level in the Region of Moderate Deviations
AbstractWe consider a random walk with zero mean and finite variance whose steps are arithmetic. The arcsine law for the time the walk reaches its...
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Moderate Deviations for Drift Parameter Estimations in Reflected Ornstein–Uhlenbeck Process
In this paper, we study the asymptotic properties of drift parameter estimations in reflected Ornstein–Uhlenbeck process, and establish their...
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The two regimes of moderate deviations for the range of a transient walk
We obtain sharp upper and lower bounds for the downward moderate deviations of the volume of the range of a random walk in dimension five and larger....
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Moderate Deviations for the Parameter Estimation in the Fractional Ornstein-Uhlenbeck Process with \(H \in (0,{1 \over 2})\)
In this paper, we study the asymptotic properties for estimators of two parameters in the drift function in the ergodic fractional Ornstein-Uhlenbeck...
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Local large deviations for periodic infinite horizon Lorentz gases
We prove optimal local large deviations for the periodic infinite horizon Lorentz gas viewed as a ℤ d -cover ( d = 1,2) of a dispersing billiard. In...
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Large and Moderate Deviations Principles and Central Limit Theorem for the Stochastic 3D Primitive Equations with Gradient-Dependent Noise
We establish the large deviations principle (LDP), the moderate deviations principle (MDP), and an almost sure version of the central limit theorem...
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Moderate Deviation Principle for Multiscale Systems Driven by Fractional Brownian Motion
In this paper, we study the moderate deviations principle (MDP) for slow–fast stochastic dynamical systems where the slow motion is governed by small...
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On the Probabilities of Large Deviations of Combinatorial Sums of Independent Random Variables That Satisfy the Linnik Condition
AbstractNew results on the asymptotic behavior of the probabilities of large deviations of combinatorial sums of independent random variables...
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Uniform Cramér moderate deviations and Berry-Esseen bounds for a supercritical branching process in a random environment
Let { Z n , n ⩾ 0} be a supercritical branching process in an independent and identically distributed random environment. We prove Cramér moderate...