8 papers
On the slow points of fractional Brownian motion
Davar Khoshnevisan, Cheuk Yin Lee
Esser and Loosveldt have recently resolved a long-standing open problem in the folklore by proving that fractional Brownian motion (fBm) has slow points in the sense of Kahane, fol…
On the spatio-temporal increments of nonlinear parabolic SPDEs and the open KPZ equation
Jingwu Hu, Cheuk Yin Lee
We study spatio-temporal increments of the solutions to nonlinear parabolic SPDEs on a bounded interval with Dirichlet, Neumann, or Robin boundary conditions. We identify the exact…
Propagation of Singularities for the Damped Stochastic Klein-Gordon Equation
Hongyi Chen, Cheuk Yin Lee
For the dimensional damped stochastic Klein-Gordon equation, we show that random singularities associated with the law of the iterated logarithm exist and propogate in the sa…
Fourier dimension of the graph of fractional Brownian motion with
Chun-Kit Lai, Cheuk Yin Lee
We prove that the Fourier dimension of the graph of fractional Brownian motion with Hurst index greater than is almost surely 1. This extends the result of Fraser and Sahlste…
Growth rate of liquidity provider's wealth in G3Ms
Cheuk Yin Lee, Shen-Ning Tung, Tai-Ho Wang
We study how trading fees and continuous-time arbitrage affect the profitability of liquidity providers (LPs) in Geometric Mean Market Makers (G3Ms). We use stochastic reflected di…
Polarity of points for Gaussian random fields in critical dimension
Youssef Hakiki, Cheuk Yin Lee, Yimin Xiao
We study the property of hitting points for a class of -valued continuous Gaussian random fields on with stationary increments, i.i.d. coordinates, and…