In this paper, we obtain the uniform estimate for discounted aggregate claims in the continuous-time renewal model of upper-tailed independent and heavy-tailed random variables. With constant interest force and constant premium rate, we establish a uniform simple asymptotic formula for ruin probability of the renewal model in the case where the initial surplus is large.
In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time.
Semiparametric models with diverging number of predictors arise in many contemporary scientific areas. Variable selection for these models consists of two components： model selection for non-parametric components and selection of significant variables for the parametric portion. In this paper, we consider a variable selection procedure by combining basis function approximation with SCAD penalty. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of tuning parameters, we establish the consistency and sparseness of this procedure.
In this paper, we consider the strong approximation for locally square-integrable martingales. In our results, the limit process may be a process with jumps. This is an extension of the former results.
