相关论文: What can be the limit in the CLT for a field of ma…

In this paper we study the central limit theorem for additive functionals of stationary Markov chains with general state space by using a new idea involving conditioning with respect to both the past and future of the chain. Practically, we…

In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for…

We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in McLeish [Ann. Probab. 5 (1977) 616--621] and motivated by Gordin [Soviet Math.…

In this paper we study the asymptotic behavior of the Gaussian quasi maximum likelihood estimator of a stationary GARCH process with heavy-tailed innovations. This means that the innovations are regularly varying with index…

The quasi-likelihood estimator and the Bayesian type estimator of the volatility parameter are in general asymptotically mixed normal. In case the limit is normal, the asymptotic expansion was derived in Yoshida (1997) as an application of…

In some earlier work we have considered extensions of Lai's (1974) law of the single logarithm for delayed sums to a multiindex setting with the same as well as different expansion rates in the various dimensions. A further generalization…

We establish a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly varying L\'{e}vy measures. The limit process is a new class of symmetric stable…

Positive $T$-martingales were developed as a general framework that extends the positive measure-valued martingales and are meant to model intermittent turbulence. We extend their scope by allowing the martingale to take complex values. We…

The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…

Consider a branching random walk in which the offspring distribution and the moving law both depend on an independent and identically distributed random environment indexed by the time.For the normalised counting measure of the number of…

In this paper, we give rates of convergence, for minimal distances and for the uniform distance, between the law of partial sums of martingale differences and thelimiting Gaussian distribution. More precisely, denoting by $P_{X}$ the law of…

We establish functional limit theorems for ergodic sums of observables with power singularities for expanding circle maps. In the regime where the observables have infinite variance, we show that when rescaled by $N^{1/s}(\ln N)^\alpha$,…

Motivated by random evolutions which do not start from equilibrium, in a recent work, Peligrad and Voln\'{y} (2018) showed that the quenched CLT (central limit theorem) holds for ortho-martingale random fields. In this paper, we study the…

Recent work in dynamic causal inference introduced a class of discrete-time stochastic processes that generalize martingale difference sequences and arrays as follows: the random variates in each sequence have expectation zero given certain…

Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment assumptions. In this paper we present several…

The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theorem. We develop a martingale expansion framework specifically…

We consider the continued fraction digits as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalized fluctuation process of the digit sums converges strongly distributional to a random variable…

Establishing central limit theorems (CLTs) for ergodic averages of Markov chains is a fundamental problem in probability and its applications. Since the seminal work~\cite{MR834478}, a vast literature has emerged on the sufficient…

We extend the notion of the associated random walk and the Wald martingale in random walks where the increments are independent and identically distributed to the more general case of stationary ergodic increments. Examples are given where…

We establish a central limit theorem for (a sequence of) multivariate martingales which dimension potentially grows with the length $n$ of the martingale. A consequence of the results are Gaussian couplings and a multiplier bootstrap for…