Convergence Rate of Wavelet Expansions of Gaussian Random Processes

This article characterizes uniform convergence rate for general classes of wavelet expansions of stationary Gaussian random processes. The convergence in probability is considered.     

Precise Asymptotics in Complete Moment Convergence of Parameter Estimator in the Gaussian Autoregressive Process

In this article, we study the precise asymptotic behaviors of the least-squares estimator in the Gaussian autoregressive process. Two kinds of complete moment convergence of this estimator can be obtained by the methods of deviation inequalities for this estimator and nonuniform Berry-Esseen bound for martingales.     

Testing Fiscal Sustainability via Strong Convergence of Gaussian Random Variables

We prove, via the Borel-Cantelli lemma, that for every sequence of Gaussian random variables the combination of convergence in expectation and decreasing variances at fractional-polynomial rate implies strong convergence. This result has an important consequence for macroeconomic stochastic infinite-horizon models: The almost sure transversality condition (i.e., fiscal sustainability with probability one) is satisfied if (a) the discounted levels of net liabilities are Gaussian-distributed with fractional-polynomially decaying variances and (b) their means converge to zero. If (a) holds but (b) fails, the transversality condition will be almost surely violated. Hence, (a) and (b) constitute a test for almost sure fiscal sustainability.     

On Empirical Processes for Ergodic Diffusions and Rates of Convergence of M-estimators

Abstract. This paper contributes to the development of empirical process theory for ergodic diffusions. We prove an entropy‐type maximal inequality for the increments of the empirical process of an ergodic diffusion. The inequality is used to study the rate of convergence of M‐estimators.