14 citations · 44 across the 33 of their papers we have counts for
21 papers · 1 filter
Gibbs measure over the cone of vector-valued discrete measures
Luca Di Persio, Yuri Kondratiev, Viktorya Vardanyan
We consider a gas whose each particle is characterised by a pair with the position and the velocity .…
Interacting particle systems with continuous spins
Viktor Bezborodov, Luca Di Persio, Martin Friesen +1
We study a general class of interacting particle systems over a countable state space where on each site the particle mass follows a stochastic differen…
Diffusion Approximation for Transport Equations with Dissipative Drifts for Time Dependent Coefficients
Luca Di Persio, Yuri Kondratiev, Viktorya Vardanyan
We consider a generalization of classical results of Freidlin and Wentzell to the case of time dependent dissipative drifts. We show the convergence of diffusions with multiplicati…
Feynman-Kac formula for BSDEs with jumps and time delayed generators associated to path-dependent nonlinear Kolmogorov equations
Luca Di Persio, Matteo Garbelli, Adrian Zălinescu
We consider a system of Forward Backward Stochastic Differential Equations (FBSDEs), with time delayed generator and driven by Lèvy-type noise. We establish a non linear Feynman Ka…
Explosion and non-explosion for the continuous-time frog model
Viktor Bezborodov, Luca Di Persio, Peter Kuchling
We consider the continuous-time frog model on . At time , there are particles at , each of which is represented by a random variable. In…
A change of measure formula for recursive conditional expectations
Luca Di Persio, Alessandro Gnoatto, Marco Patacca
In this paper, we derive a representation for the value process associated to the solutions of FBSDEs in a jump-diffusion setting under multiple probability measures. Motivated by…
Time-Delayed Generalized BSDEs
Luca Di Persio, Matteo Garbelli, Lucian Maticiuc +1
We prove the existence and uniqueness of the solution of a BSDE with time-delayed generators in the small delay setting (or equivalently small Lipschitz constant), which employs th…
The continuous-time frog model can spread arbitrarily fast
Viktor Bezborodov, Luca Di Persio, Tyll Krueger
The aim of this work is to demonstrate that the continuous-time frog model can spread arbitrary fast. The set of sites visited by an active particle can become infinite in a finite…
Shape theorem for a one-dimensional growing particle system with a bounded number of occupants per site
Viktor Bezborodov, Luca Di Persio, Tyll Krueger
We consider a one-dimensional discrete-space birth process with a bounded number of particle per site. Under the assumptions of the finite range of interaction, translation invaria…
Stochastic port--Hamiltonian systems
Francesco Cordoni, Luca Di Persio, Riccardo Muradore
In the present work we formally extend the theory of port-Hamiltonian systems to include random perturbations. In particular, suitably choosing the space of flow and effort variabl…
Spatial growth processes with long range dispersion: microscopics, mesoscopics, and discrepancy in spread rate
Viktor Bezborodov, Luca Di Persio, Tyll Krueger +1
We consider the speed of propagation of a {continuous-time continuous-space} branching random walk with the additional restriction that the birth rate at any spatial point cannot e…
-Nash equilibrium in stochastic differential games with mean-field interaction and controlled jumps
Chiara Benazzoli, Luciano Campi, Luca Di Persio
We consider a symmetric -player nonzero-sum stochastic differential game with controlled jumps and mean-field type interaction among the players. Each player minimizes some expe…
Mean field games with controlled jump-diffusion dynamics: Existence results and an illiquid interbank market model
Chiara Benazzoli, Luciano Campi, Luca Di Persio
We study a family of mean field games with a state variable evolving as a multivariate jump diffusion process. The jump component is driven by a Poisson process with a time-depende…
Maximal irreducibility measure for spatial birth-and-death processes
Viktor Bezborodov, Luca Di Persio
We prove that under certain general conditions on the birth and death rates the Lebesgue-Poisson measure is a maximal irreducibility measure for the spatial birth-and-death process…
Asymptotic shape and the speed of propagation of continuous-time continuous-space birth processes
Viktor Bezborodov, Luca Di Persio, Tyll Krueger +2
We formulate and prove a shape theorem for a continuous-time continuous-space stochastic growth model under certain general conditions. Similarly to the classical lattice growth mo…
Option pricing with fractional stochastic volatility and discontinuous payoff function of polynomial growth
Viktor Bezborodov, Luca Di Persio, Yuliya Mishura
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework cha…
A stochastic approach to path-dependent nonlinear Kolmogorov equations via BSDEs with time-delayed generators and applications to finance
Francesco Cordoni, Luca Di Persio, Lucian Maticiuc +1
We prove the existence of a viscosity solution of the following path dependent nonlinear Kolmogorov equation: \[ \begin{cases} \partial_{t}u(t,ϕ)+\mathcal{L}u(t,ϕ)+f(t,ϕ,u(t,ϕ),\pa…
A nonlinear Kolmogorov equation for stochastic functional delay differential equations with jumps
Francesco Cordoni, Luca Di Persio, Immacolata Oliva
We consider a stochastic functional delay differential equation, namely an equation whose evolution depends on its past history as well as on its present state, driven by a pure di…
Spatial birth-and-death processes with a finite number of particles
Viktor Bezborodov, Luca Di Persio
Spatial birth-and-death processes with time dependent rates are obtained as solutions to certain stochastic equations. The existence, uniqueness, uniqueness in law and the strong M…
A class of Lévy driven SDEs and their explicit invariant measures
Sergio Albeverio, Luca Di Persio, Elisa Mastrogiacomo +1
We describe a class of explicit invariant measures for both finite and infinite dimensional Stochastic Differential Equations (SDE) driven by Lévy noise. We first discuss in detail…
Explicit invariant measures for infinite dimensional SDE driven by Lévy noise with dissipative nonlinear drift I
Sergio Albeverio, Luca Di Persio, Elisa Mastrogiacomo +1
We stu\dd y a class of nonlinear stochastic partial differential equations with dissipative nonlinear drift, driven by Lévy noise. Our work is divided in two parts. In the present…