Mathematical Finance, Stochastic Analysis and Machine Learning Seminar By Tyrone Duncan: Some Properties and Applications of Rosenblatt Processes
Tyrone Duncan, University of Kansas
Some Properties and Applications of Rosenblatt Processes
Rosenblatt processes are a family of continuous, non-Gaussian processes that are defined by double Wiener-Ito integrals with singular integrands so they can be viewed as a natural generalization from the family of fractional Brownian motions. The Rosenblatt processes seem to have attractive properties for some models of noise in physical systems where often Gaussian processes cannot be justified from the empirical evidence. The Rosenblatt processes have a stochastic calculus that is described and allows for various applications. Explicit solutions of some optimization (control) problems for linear controlled equations are given where the noise is a Rosenblatt process. These problems can have both finite and infinite time horizon quadratic cost functionals.
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Mathematical Finance, Stochastic Analysis and Machine Learning