To investigate the consistency challenges in parameter estimation for explosive-regime mean-reverting diffusion processes ( & rhov;>1 ) under discrete-time observations, this research develops a novel martingale-based Euler-maximum likelihood estimation (E-MLE) methodology for the nonlinear mean-reverting stochastic model with & rhov;=3/2 . Specifically, we first establish the existence of a global positive, non-explosive solution, guaranteeing global positivity of the process, and then derive uniform bounds on its negative moments together with the finiteness of its low-order positive moments; we further show that positive moments of order >= 2 are not uniformly bounded, so that the standard linear-growth existence-uniqueness and moment theorems do not apply, the diffusion coefficient growing super-linearly. Next, explicit estimator forms are derived using the E-MLE approach, and their strong consistency properties are demonstrated through martingale arguments, including the strong law of large numbers for martingales, combined with the ergodic theorem and the above negative-moment bounds. After that, numerical simulations are used to verify the effectiveness of the estimators by evaluating their errors relative to the true parameter values across different error measures under various volatility regimes. Finally, an out-of-sample validation on Moroccan and Hungarian interest-rate data shows that, among the competing models on these datasets, the proposed estimators deliver the lowest one-step out-of-sample forecasting error and a well-calibrated 90% predictive band on held-out data, while remaining well-posed with positive parameters. This has practical implications for financial forecasting and emerging-market analysis.
This work explores fractional impulsive partial stochastic differential systems driven by tempered fractional Brownian motion involving time varying delay and non-instantaneous impulses in separable Hilbert spaces. We looked into several criteria to guarantee the existence mild solutions using fractional calculus technique, stochastic analysis, suitable fixed point theorems, and the Hausdorff measure of noncompactness. The derived result in this work is new in the sense that it generalizes many of the existing results in the literature, more precisely for tempered fractional Brownian motion, time varying delay and non-instantaneous impulsive case of psi -Caputo derivative in the stochastic settings. In conclusion, we provide some examples to illustrate the findings.
In this correspondence, we study the relationship between the concepts of complete convergence, complete moment convergence, and complete integral convergence. More specifically, complete moment convergence of order q > 0 is shown to be equivalent to complete integral convergence of the same order. A triumvirate of conditions are provided for complete moment convergence of the row sums from an array of rowwise independent random variables. Several illustrative examples are presented.
