The product of two zero mean correlated normal random variables, and more generally the sum independent copies such has received much attention in statistics literature appears many application areas. However, important distributional properties are yet to be recorded. This review paper fills this gap by providing basic theory for variables. Properties covered include probability cumulative dis...

We consider a family of continuous processes {X?}?>0 which are measurable with respect to white noise measure, take values in the space functions C([0,1]d:R), and have Wiener chaos expansion X?= ?n=0??nIn(fn?). provide sufficient conditions for large deviations principle hold thereby refreshing problem left open by Pérez–Abreu (1993) Brownian motion case. The proof is based on weak convergence ...

This work is concerned with forest and cumulant type expansions of general random variables on a filtered probability space. We establish “broken exponential martingale” expansion that generalizes unifies the exponentiation result Alòs, Gatheral, Radoičić (SSRN’17; Quant. Finance 20 (2020) 13–27) recursion formula Lacoin, Rhodes, Vargas (arXiv; (2019)). Specifically, we exhibit two previous res...

In this paper we obtain some new Strichartz estimates for the wave propagator e i t − Δ in context of Wiener amalgam spaces. While it is well understood Schrödinger case, nothing known about propagator. This because there no such thing as an explicit formula integral kernel unlike case. To overcome lack, instead approach by rephrasing oscillatory involving Bessel functions and then carefully ma...

Many interesting physical theories have analytic classical actions. We show how Feynman’s path integral may be defined non-perturbatively, for such theories, without a Wick rotation to imaginary time. start by introducing class of smooth regulators which render interference integrals absolutely convergent and thus unambiguous. The analyticity the allows us use Cauchy’s theorem deform integratio...