2 citations · 5 across the 14 of their papers we have counts for
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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…
Almost periodicity as a path property for -adic self-similar processes with stationary increments
Yi Shen, Zhenyuan Zhang
Shen and Zhang (2021) showed that almost periodicity naturally arises in the spectral representation of discrete-time -adic self-similar processes with stationary increments. In…
Quadratic-form Optimal Transport
Ruodu Wang, Zhenyuan Zhang
We introduce the framework of quadratic-form optimal transport (QOT), whose transport cost has the form for some coupling between two m…
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…
Weierstrass Bridges
Alexander Schied, Zhenyuan Zhang
We introduce a new class of stochastic processes called fractional Wiener-Weierstrass bridges. They arise by applying the convolution from the construction of the classical, fracta…
Martingale Transports and Monge Maps
Marcel Nutz, Ruodu Wang, Zhenyuan Zhang
It is well known that martingale transport plans between marginals are never given by Monge maps -- with the understanding that the map is over the first marginal , or…
Consensus on Dynamic Stochastic Block Models: Fast Convergence and Phase Transitions
Haoyu Wang, Jiaheng Wei, Zhenyuan Zhang
We introduce two models of consensus following a majority rule on time-evolving stochastic block models (SBM), in which the network evolution is Markovian or non-Markovian. Under t…
A limit theorem for Bernoulli convolutions and the -variation of functions in the Takagi class
Xiyue Han, Alexander Schied, Zhenyuan Zhang
We consider a probabilistic approach to compute the Wiener--Young -variation of fractal functions in the Takagi class. Here, the -variation is understood as a generalization…
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…