Limit Theorems for Conservative Flows on Multiple Stochastic Integrals

We consider a stationary sequence $$(X_n)$$ constructed by multiple stochastic integral and an infinite-measure conservative dynamical system. The random measure defining the is non-Gaussian infinitely divisible has finite variance. Some additional assumptions on system give rise to parameter $$\beta \in (0,1)$$ quantifying conservativity of This $$ together with order determines decay rate covariance . goal paper establish limit theorems for partial sum process obtain central theorem Brownian motion as when decays fast enough, well non-central fractional or Rosenblatt slowly enough.