5 papers
Decorated stable -adic self-similar processes with stationary increments
Yi Shen, Zhenyuan Zhang
We construct new classes of examples of self-similar processes with stationary increments indexed by via stable integrals. Classical constructions arise from the real…
Sample Path Properties of the Fractional Wiener--Weierstrass Bridge
Alexander Schied, Zhenyuan Zhang
Fractional Wiener--Weierstrass bridges are a class of Gaussian processes that arise from replacing the trigonometric function in the construction of classical Weierstrass functions…
A probabilistic approach to the -variation of classical fractal functions with critical roughness
Xiyue Han, Alexander Schied, Zhenyuan Zhang
We consider Weierstraß and Takagi-van der Waerden functions with critical degree of roughness. In this case, the functions have vanishing variation for all bu…
On the variation of a class of fractal functions
Alexander Schied, Zhenyuan Zhang
The concept of the variation of a continuous function along a refining sequence of partitions is the key to a pathwise Itô integration theory with integrator $f…
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…