Analysis of the Rosenblatt process
Ciprian A. Tudor
Abstract
We analyze the Rosenblatt process which is a selfsimilar process with stationary increments and which appears as limit in the so-called Non Central Limit Theorem (Dobrushin and Major (1979), Taqqu (1979)). This process is non-Gaussian and it lives in the second Wiener chaos. We give its representation as a Wiener-Itô multiple integral with respect to the Brownian motion on a finite interval and we develop a stochastic calculus with respect to it by using both pathwise type calculus and Malliavin calculus.
Create a lesson
Related papers
Distribution-constrained optimal multiple stopping: the Root-type solution
Shuoqing Deng, Daxin Huang
Universality and sharp thresholds for ellipsoid fitting
Frederic Koehler, Youngtak Sohn
Local Laws and Edge Universality for Noncentral Sample Covariance Matrices
Can Hu, Jiang Hu, Zhidong Bai
Well-posedness and regularity of stochastic heat equations on moving domains
Chongyang Ren, Tusheng Zhang
Traveling Waves in Equity Markets with Rank-Based Entry and Exit
Graeme Baker, Caroline Smyth
An approximate zero bias transformation for random sums: Applications to sampling with outliers, auto insurance, and generative AI
Wasamon Jantai, Nathakhun Wiroonsri