arXiv subjects

Mattia Turra

Publications and source records attributed to Mattia Turra.

3 recordsLinked to original sources

arXiv2022

A singular integration by parts formula for the exponential Euclidean QFT on the plane

We give a novel characterization of the Euclidean quantum field theory with exponential interaction $ν$ on $\mathbb{R}^2$ through a renormalized integration by parts (IbP) formula, or otherwise said via an Euclidean Dyson-Schwinger equation for expected values of observables. In order to obtain the well-posedness of the singular IbP problem, we import some ideas used to analyse singular SPDEs and we require the measure to "look like" the Gaussian free field (GFF) in the sense that a suitable Wasserstein distance from the GFF is finite. This guarantees the existence of a nice coupling with the GFF which allows to control the renormalized IbP formula.

math.PR↗

arXiv2021

Noether theorem in stochastic optimal control problems via contact symmetries

We establish a generalization of Noether theorem for stochastic optimal control problems. Exploiting the tools of jet bundles and contact geometry, we prove that from any (contact) symmetry of the Hamilton-Jacobi-Bellman equation associated to an optimal control problem it is possible to build a related local martingale. Moreover, we provide an application of the theoretical results to Merton's optimal portfolio problem, showing that this model admits infinitely many conserved quantities in the form of local martingales.

math.OC↗

arXiv2018

Existence and extinction in finite time for Stratonovich gradient noise porous media equations

We study existence and uniqueness of distributional solutions to the stochastic partial differential equation $dX - ( νΔX + Δψ(X) ) dt = \sum_{i=1}^N \langle b_i, \nabla X \rangle \circ dβ_i$ in $]0,T[ \times \mathcal{O}$, with $X(0) = x(ξ)$ in $\mathcal{O}$ and $X = 0$ on $]0,T[ \times \partial \mathcal{O}$. Moreover, we prove extinction in finite time of the solutions in the special case of fast diffusion model and of self-organized criticality model.

math.PR↗