25 citations · 105 across the 16 of their papers we have counts for
18 papers
Random rotational invariance of integration by parts formulas within a Bismut-type approach
Susanna Dehò, Francesco C. De Vecchi, Paola Morando +1
The stochastic rotational invariance of an integration by parts formula inspired by the Bismut approach to Malliavin calculus is proved in the framework of the Lie symmetry theory…
Invariant Gibbs measure for Anderson nonlinear wave equation
Nikolay Barashkov, Francesco C. De Vecchi, Immanuel Zachhuber
We study the Gaussian measure whose covariance is related to the Anderson Hamiltonian operator, proving that it admits a regular coupling to the (standard) Gaussian free field expl…
Integration by parts formulas and Lie's symmetries of SDEs
Francesco C. De Vecchi, Paola Morando, Stefania Ugolini
A strong quasi-invariance principle and a finite-dimensional integration by parts formula as in the Bismut approach to Malliavin calculus are obtained through a suitable applicatio…
Elliptic stochastic quantization of Sinh-Gordon QFT
Nikolay Barashkov, Francesco C. De Vecchi
The (elliptic) stochastic quantization equation for the (massive) model, for the charged parameter in the regime (i.e. ), is studied. We prove the ex…
Noether theorem in stochastic optimal control problems via contact symmetries
Francesco C. De Vecchi, Elisa Mastrogiacomo, Mattia Turra +1
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)…
Grassmannian stochastic analysis and the stochastic quantization of Euclidean Fermions
Sergio Albeverio, Luigi Borasi, Francesco C. De Vecchi +1
We introduce a stochastic analysis of Grassmann random variables suitable for the stochastic quantization of Euclidean fermionic quantum field theories. Analysis on Grassmann algeb…
Mean-field limit for a class of stochastic ergodic control problems
Sergio Albeverio, Francesco C. De Vecchi, Andrea Romano +1
We study a family of McKean-Vlasov (mean-field) type ergodic optimal control problems with linear control, and quadratic dependence on control of the cost function. For this class…
A note on the continuity in the Hurst index of the solution of rough differential equations driven by a fractional Brownian motion
Francesco C. De Vecchi, Luca M. Giordano, Daniela Morale +1
Within the rough path framework we prove the continuity of the solution to random differential equations driven by fractional Brownian motion with respect to the Hurst parameter $H…
Symmetries of Stochastic Differential Equations using Girsanov transformations
Francesco C. De Vecchi, Paola Morando, Stefania Ugolini
Aiming at enlarging the class of symmetries of an SDE, we introduce a family of stochastic transformations able to change also the underlying probability measure exploiting Girsano…
Strong Kac's chaos in the mean-field Bose-Einstein Condensation
Sergio Albeverio, Francesco C. De Vecchi, Andrea Romano +1
A stochastic approach to the (generic) mean-field limit in Bose-Einstein Condensation is described and the convergence of the ground state energy as well as of its components are e…
Random transformations and invariance of semimartingales on Lie groups
Sergio Albeverio, Francesco C. De Vecchi, Paola Morando +1
Invariance properties of semimartingales on Lie groups under a family of random transformations are defined and investigated, generalizing the random rotations of the Brownian moti…
A note on symmetries of diffusions within a martingale problem approach
Francesco C. De Vecchi, Paola Morando, Stefania Ugolini
A geometric reformulation of the martingale problem associated with a set of diffusion processes is proposed. This formulation, based on second order geometry and Ito integration o…
A symmetry-adapted numerical scheme for SDEs
Francesco C. De Vecchi, Andrea Romano, Stefania Ugolini
We propose a geometric numerical analysis of SDEs admitting Lie symmetries which allows us to individuate a symmetry adapted coordinates system where the given SDE has notable inva…
Reduction and reconstruction of stochastic differential equations via symmetries
Francesco C. De Vecchi, Paola Morando, Stefania Ugolini
An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented and a natural definition of reconstruction,…
The geometry of differential constraints for a class of evolution PDEs
Francesco C. De Vecchi, Paola Morando
The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized…
Solvable structures for evolution PDEs admitting differential constraints
Francesco C. De Vecchi, Paola Morando
Solvable structures are exploited in order to find families of explicit solutions to evolution PDEs admitting suitable differential constraints. The effectiveness of the method is…
Symmetries of Stochastic Differential Equations: a geometric approach
Francesco C. De Vecchi, Paola Morando, Stefania Ugolini
A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence be…
Entropy Chaos and Bose-Einstein Condensation
Sergio Albeverio, Francesco C. De Vecchi, Stefania Ugolini
We prove the entropy-chaos property for the system of N undistinguishable interacting diffusions rigorously associated with the ground state of N trapped Bose particles in the Gros…