A note on the matrix renewal function

A Note on Markov-renewal Programming

Note on Fuzzy Random Renewal Process and Renewal Rewards Process

Recently, Zhao et al. [Fuzzy Optimization and Decision Making (2007) 6, 279-295] characterized the interarrival times as fuzzy random variables and presented a fuzzy random elementary renewal theorem on the limit value of the expected renewal rate of the process in the fuzzy random renewal process. They also depicted both the interarrival times and rewards are depicted as fuzzy random variables...

A note on matrix rigidity

In this paper we give an explicit construction of n × n matrices over finite fields which are somewhat rigid, in that if we change at most k entries in each row, its rank remains at least Cn(logq k)/k, where q is the size of the field and C is an absolute constant. Our matrices satify a somewhat stronger property, we which explain and call “strong rigidity.” We introduce and briefly discuss str...

A note on a class of delayed renewal risk processes

The Gerber-Shiu discounted penalty function is considered for a class of delayed renewal risk processes. Special cases of the model include the stationary renewal risk model and the situation where the time until the first claim is exponentially distributed. A mathematically tractable formula is derived for the Gerber-Shiu function, and consequently for quantities associated with the deficit at...

A Note on the Smooth Estimator of the Quantile Function with Left-Truncated Data

This note focuses on estimating the quantile function based on the kernel smooth estimator under a truncated dependent model. The Bahadurtype representation of the kernel smooth estimator is established, and from the Bahadur representation it can be seen that this estimator is strongly consistent.