4 papers · 1 filter
An aggregated model for Karlin stable processes
Yi Shen, Yizao Wang, Na Zhang
An aggregated model is proposed, of which the partial-sum process scales to the Karlin stable processes recently investigated in the literature. The limit extremes of the proposed…
On discrete-time self-similar processes with stationary increments
Yi Shen, Zhenyuan Zhang
In this paper we study the self-similar processes with stationary increments in a discrete-time setting. Different from the continuous-time case, it is shown that the scaling funct…
A Noether theorem for random locations
Shunlong Luo, Jie Shen, Yi Shen
We propose a unified framework for random locations exhibiting some probabilistic symmetries such as stationarity, self-similarity, etc. A theorem of Noether's type is proved, whic…
Location of the Path Supremum for Self-similar Processes with Stationary Increments
Yi Shen
In this paper we consider the distribution of the location of the path supremum in a fixed interval for self-similar processes with stationary increments. To this end, a point proc…