7 papers
Unimodal maps perturbed by heteroscedastic noise: an application to a financial systems
F. Lillo, G. Livieri, S. Marmi +2
We investigate and prove the mathematical properties of a general class of one-dimensional unimodal smooth maps perturbed with a heteroscedastic noise. Specifically, we investigate…
Analysis of bank leverage via dynamical systems and deep neural networks
Fabrizio Lillo, Giulia Livieri, Stefano Marmi +2
We consider a model of a simple financial system consisting of a leveraged investor that invests in a risky asset and manages risk by using Value-at-Risk (VaR). The VaR is estimate…
On isomorphism problem for von Neumann flows with one discontinuity
Adam Kanigowski, Anton V. Solomko
A von Neumann flow is a special flow over an irrational rotation of the circle and under a piecewise roof function with a non-zero sum of jumps. We prove that the absolute va…
On rank of von Neumann special flows
Adam Kanigowski, Anton V. Solomko
We prove that special flows over an ergodic rotation of the circle under a roof function with one discontinuity do not have local rank one. In particular, any such flow has i…
Simple mixing actions with uncountably many prime factors
Alexandre I. Danilenko, Anton V. Solomko
Via (C,F)-construction we produce a 2-fold simple mixing transformation which has uncountably many non-trivial proper factors and all of them are prime.
New spectral multiplicities for ergodic actions
Anton V. Solomko
Let G be a locally compact second countable Abelian group. Given a measure preserving action T of G on a standard probability space, let M(T) denote the set of essential values of…
Ergodic Abelian actions with homogeneous spectrum
Alexandre I. Danilenko, Anton V. Solomko
It is shown that for each and for a wide class of Abelian non-compact locally compact second countable groups including all infinite countable discrete ones and $\Bbb R^{…