Anna Mazzucato, Major Field Member Alexei Novikov, Chair & Dissertation Advisor Guodong Pang, Outside Unit & Field Member Alexei Novikov, Professor in Charge/Director of Graduate Studies Iouri Soukhov, Major Field Member
Keywords:
Stochastic Processes Differential Equations
Abstract:
The long-time behavior of dynamical systems driven by fractional Brownian motions is an interesting and challenging problem. The main difficulty of analysis is that fractional Brownian motion is neither a Markov process nor a semimartingale. Therefore, the machinery of classical stochastic calculus is not suitable to analyze such systems. This dissertation considers Hamiltonian systems driven by algebraically decorrelating noises, which are approximations to fractional Brownian motion noises. The main result of the thesis is that in certain conditions, the long-time behavior of the Hamiltonian does not depend on the memory-property of the driven noises: the limiting process is a diffusion. In other words, the Hamiltonian dynamics are strong enough to overcome long-range correlations of the noise and make the system converge. The goal is to establish a universal limit independent of the nature of the noise.
