Moderate deviations principle for products of sums of random variables

Let(Xn)n≥1 be a sequence of independent identically distributed(i.i.d.) positive random variables with EX1 = μ,Var(X1) = σ2.In the present paper,we establish the moderate deviations principle for the products of partial sums(πnk=1Sk/n!μn)1/(γbn√(2n))1where γ = σ/μ denotes the coefficient of variation and(bn) is the moderate deviations scale.

Moderate Deviations for Marked Hawkes Processes

We consider a linear Hawkes process with random marks. Some limit theorems have been studied by Karabash and Zhu [Stoch. Models, 31,433-451 （2015）]. In this paper, we obtain a moderate deviation principle for marked Hawkes processes.

Moderate deviations for Euler-Maruyama approximation of Hull-White stochastic volatility model

We consider the Euler-Maruyama discretization of stochastic volatility model dSt = σtStdWt, dσt = ωσtdZt, t ∈ [0, T], which has been widely used in financial practice, where Wt, Zt, t ∈ [0, T], are two uncorrelated standard Brownian motions. Using asymptotic analysis techniques, the moderate deviation principles for log Sn （or log ｜Sn｜ in case Sn is negative） are obtained as n → ∞ under different discretization schemes for the asset price process St and the volatility process σt. Numerical simulations are presented to compare the convergence speeds in different schemes.

Moderate deviation for super-Brownian motion with immigration

We prove a moderate deviation principle for a super-Brownian motion with immigration of all dimensions, and consequently fill the gap between the central limit theorem and large deviation principle.

Moderate deviation and central limit theorem for stochastic differential delay equations with polynomial growth

Employing the weak convergence method, based on a variational representation for expected values of positive functionals of a Brownian motion, we investigate moderate deviation for a class of stochastic differential delay equations with small noises, where the coefficients are allowed to be highly nonlinear growth with respect to the variables. Moreover, we obtain the central limit theorem for stochastic differential delay equations which the coefficients are polynomial growth with respect to the delay variables.

Asymptotic behavior of estimators of entropic risk measures under asymmetric Laplace law

In this paper,we study several asymptotic behaviors of the estimators of convex and coherent entropic risk measures.First,the moderate deviation principles of the estimators are given.Second,the central limit theorems of the estimators are given.Finally,several simulation results are given to support our main conclusions.