Let (ξ i, F i) i≥ 1 be a sequence of martingale differences. Set X n=∑ i= 1 n ξ i and⟨ X⟩ n=∑
i= 1 n E (ξ i 2| F i− 1). We prove Cramér's moderate deviation expansions for P (X n/⟨ X⟩ n≥ …

Abstract Renz [14], Ouchti [13], El Machkouri and Ouchti [3] and Mourrat [12] have
established some tight bounds on the rate of convergence in the central limit theorem for …

Let (X i) i≥ 1 be a stationary sequence. Denote m=⌊ n α⌋, 0< α< 1, and k=⌊ n∕ m⌋,
where⌊ a⌋ stands for the integer part of a. Set S j∘=∑ i= 1 m X m (j− 1)+ i, 1≤ j≤ k, and (V …

Let $(\xi_i,\mathcal {F} _i) _ {i\geq1} $ be a sequence of martingale differences. Set $
X_n=\sum_ {i= 1}^ n\xi_i $ and $\langle X\rangle_n=\sum_ {i= 1}^ n\mathbf {E}(\xi_i …

Let Z n, n⩾ 0 be a supercritical branching process in an independent and identically
distributed random environment. We prove Cramér moderate deviations and Berry-Esseen …

In this paper, we establish normalized and self-normalized Cramér-type moderate
deviations for the Euler-Maruyama scheme for SDE. Due to our results, Berry-Esseen's …

CRAMÉR TYPE MODERATE DEVIATIONS FOR RANDOM FIELDS Page 1 J. Appl. Prob. 56,
223–245 (2019) doi:10.1017/jpr.2019.15 © Applied Probability Trust 2019 CRAMÉR TYPE …

We show sharp bounds for probabilities of large deviations for sums of independent random
variables satisfying Bernstein's condition. One such bound is very close to the tail of the …

We establish Cramér-type moderate deviation theorems for the sums of locally dependent
random variables and combinatorial central limit theorems. Optimal error bounds and …

➢ Keywords: Causal inference, decision-making, and experimental design.∎ Treatment arm
(arm/treatment/policy). ex. drugs, advertisements, and economic policies.• Each treatment …