arXiv subjects

Marta Leocata

Publications and source records attributed to Marta Leocata.

16 recordsLinked to original sources

arXiv2026

Understanding the householder solar panel consumer: A Markovian model and its societal implications

Household adoption of rooftop photovoltaic (PV) systems is central to the green energy transition, yet diffusion depends on social influence and behavioral biases, as well as payback economics. This study develops a parsimonious Markovian model in which households move sequentially from being unengaged (Carbon) to informed, to planning, and finally to adoption (Green). Transition rates are micro-founded by two mechanisms: (i) social contagion/communication, proxied by the current share of adopters, and (ii) economic profitability, proxied by payback time computed from a Net Present Value framework. Novel to this diffusion setting, bounded rationality is introduced via hyperbolic discounting, creating a procrastination loop that delays adoption even when PV is economically attractive in a long-run perspective. Calibrated on the Italian residential PV diffusion path (2006-2020) and assessed in national and regional applications, the model reproduces observed trajectories and enables forward-looking scenario analysis (2020-2026). Results show that policies yielding similar payback improvements can produce different outcomes once present bias is accounted for and that behaviorally informed intervention are stronger. The findings contribute a micro-to-macro bridge between behavioral economics and technology diffusion modeling and imply that effective policy portfolios (and PV business models) should complement incentives with commitment devices and social-norm peer strategies to accelerate PV uptake and its spillover emissions benefits.

physics.soc-ph↗

arXiv2026

Network-Based Optimal Control of Pollution Growth

This paper studies a model for the optimal control (by a centralized economic agent which we call the planner) of pollution diffusion over time and space. The controls are the investments in production and depollution and the goal is to maximize an intertemporal utility function. The main novelty is the fact that the spatial component has a network structure. Moreover, in such a time-space setting we also analyze the trade-off between the use of green or non-green technologies: this also seems to be a novelty in such a setting. Extending methods of previous papers, we can solve explicitly the problem in the case of linear costs of pollution.

econ.TH↗

arXiv2025

Optimal policies for environmental assets under spatial heterogeneity and global awareness

The aim of this paper is to formulate and study a stochastic model for the management of environmental assets in a geographical context where in each place the local authorities take their policy decisions maximizing their own welfare, hence not cooperating each other. A key feature of our model is that the welfare depends not only on the local environmental asset, but also on the global one, making the problem much more interesting but technically much more complex to study, since strategic interaction among players arise. We study the problem first from the $N$-players game perspective and find open and closed loop Nash equilibria in explicit form. We also study the convergence of the $N$-players game (when $n\to +\infty$) to a suitable Mean Field Game whose unique equilibrium is exactly the limit of both the open and closed loop Nash equilibria found above, hence supporting their meaning for the game. Then we solve explicitly the problem from the cooperative perspective of the social planner and compare its solution to the equilibria of the $N$-players game. Moreover we find the Pigouvian tax which aligns the decentralized closed loop equilibrium to the social optimum.

math.OC↗

arXiv2025

Structural properties in the diffusion of the solar photovoltaic in Italy: individual people/householder vs firms

This paper develops two mathematical models to understand subjects' behavior in response to the urgency of a change and inputs from governments e.g., (subsides) in the context of the diffusion of the solar photovoltaic in Italy. The first model is a Markovian model of interacting particle systems. The second one, instead, is a Mean Field Game model. In both cases, we derive the scaling limit deterministic dynamics, and we compare the latter to the Italian solar photovoltaic data. We identify periods where the first model describes the behavior of domestic data well and a period where the second model captures a particular feature of data corresponding to companies. The comprehensive analysis, integrated with a philosophical inquiry focusing on the conceptual vocabulary and correlative implications, leads to the formulation of hypotheses about the efficacy of different forms of governmental subsidies.

physics.soc-ph↗

arXiv2025

Derivation of the viscoelastic stress in Stokes flows induced by non-spherical Brownian rigid particles through homogenization

We consider a microscopic model of $n$ identical axis-symmetric rigid Brownian particles suspended in a Stokes flow. We rigorously derive in the homogenization limit of many small particles a classical formula for the viscoelastic stress that appears in so-called Doi models which couple a Fokker-Planck equation to the Stokes equations. We consider both Deborah numbers of order $1$ and very small Deborah numbers. Our microscopic model contains several simplifications, most importantly, we neglect the time evolution of the particle centers as well as hydrodynamic interaction for the evolution of the particle orientations. The microscopic fluid velocity is modeled by the Stokes equations with given torques at the particles in terms of Stratonovitch noise. We give a meaning to this PDE in terms of an infinite dimensional Stratonovitch integral. This requires the analysis of the shape derivatives of the Stokes equations in perforated domains, which we accomplish by the method of reflections.

math.AP↗

arXiv2024

A Mean Field Game approach for pollution regulation of competitive firms

We develop a model based on mean-field games of competitive firms producing similar goods according to a standard AK model with a depreciation rate of capital generating pollution as a byproduct. Our analysis focuses on the widely-used cap-and-trade pollution regulation. Under this regulation, firms have the flexibility to respond by implementing pollution abatement, reducing output, and participating in emission trading, while a regulator dynamically allocates emission allowances to each firm. The resulting mean-field game is of linear quadratic type and equivalent to a mean-field type control problem, i.e., it is a potential game. We find explicit solutions to this problem through the solutions to differential equations of Riccati type. Further, we investigate the carbon emission equilibrium price that satisfies the market clearing condition and find a specific form of FBSDE of McKean-Vlasov type with common noise. The solution to this equation provides an approximate equilibrium price. Additionally, we demonstrate that the degree of competition is vital in determining the economic consequences of pollution regulation.

q-fin.MF↗

arXiv2024

Global solutions to quadratic systems of stochastic reaction-diffusion equations in space-dimension two

We prove the existence of global-in-time regular solutions to a system of stochastic quadratic reaction-diffusion equations. Global-in-time existence is based on a $L^\infty$-estimate obtained by an approach {à} la De Giorgi, as in [GoudonVasseur10]. The adaptation of this technique to the stochastic case requires in its final step an $L^2\ln(L^2)$-bound, furnished by an estimate by duality on the entropy inequality, as in [DesvillettesFellnerPierreVovelle07]. In our stochastic context, and similarly to [DebusscheRoselloVovelle2021], we need to solve a backward SPDE to exploit the duality technique

math.AP↗

arXiv2023

Optimal Planning in Habit Formation Models with Multiple Goods

In this paper, on the line e.g. of [COW00]) we investigate a model with habit formation and two types of substitute goods. Such family of models, even in the case of 1 good, are difficult to study since their utility function is not concave in the interesting cases (see e.g. [BG20]), hence the first order conditions are not sufficient. We introduce and explain the model and provide some first results using the dynamic programming approach. Such results will form a solid ground over which a deep study of the features of the solutions can be performed.

math.OC↗

arXiv2023

An optimal control problem with state constraints in a spatio-temporal economic growth model on networks

We introduce a spatial economic growth model where space is described as a network of interconnected geographic locations and we study a corresponding finite-dimensional optimal control problem on a graph with state constraints. Economic growth models on networks are motivated by the nature of spatial economic data, which naturally possess a graph-like structure: this fact makes these models well-suited for numerical implementation and calibration. The network setting is different from the one adopted in the related literature, where space is modeled as a subset of a Euclidean space, which gives rise to infinite dimensional optimal control problems. After introducing the model and the related control problem, we prove existence and uniqueness of an optimal control and a regularity result for the value function, which sets up the basis for a deeper study of the optimal strategies. Then, we focus on specific cases where it is possible to find, under suitable assumptions, an explicit solution of the control problem. Finally, we discuss the cases of networks of two and three geographic locations.

math.OC↗

arXiv2022

A Stochastic Model of Economic Growth in Time-Space

We deal with an infinite horizon, infinite dimensional stochastic optimal control problem arising in the study of economic growth in time-space. Such problem has been the object of various papers in deterministic cases when the possible presence of stochastic disturbances is ignored. Here we propose and solve a stochastic generalization of such models where the stochastic term, in line with the standard stochastic economic growth models, is a multiplicative one, driven by a cylindrical Wiener process. The problem is studied using the Dynamic Programming approach. We find an explicit solution of the associated HJB equation and, using a verification type result, we prove that such solution is the value function and we find the optimal feedback strategies. Finally we use this result to study the asymptotic behavior of the optimal trajectories.

math.OC↗

arXiv2022

Habits and demand changes after COVID-19

In this paper, we investigate how the COVID-19 pandemics and more precisely the lockdown of a sector of the economy may have changed our habits and, there-fore, altered the demand of some goods even after the re-opening. In a two-sector infinite horizon economy, we show that the demand of the goods produced by the sector closed during the lockdown could shrink or expand with respect to their pre-pandemic level depending on the length of the lockdown and the relative strength of the satiation effect and the substitutability effect. We also provide conditions under which this sector could remain inactive even after the lockdown as well as an insight on the policy which should be adopted to avoid this outcome.

econ.TH↗

arXiv2020

On the Macroscopic limit of Brownian Particles with local interaction

An interacting particle system made of diffusion processes with local interaction is considered and the macroscopic limit to a nonlinear PDE is investigated. Few rigorous results exists on this problem and in particular the explicit form of the nonlinearity is not known. The paper reviews this subject, some of the main ideas to get the limit nonlinear PDE and provides both heuristic and numerical informations on the precise form of the nonlinearity which are new with respect to the literature and coherent with the few known informations.

math.PR↗

arXiv2019

A particle system approach to aggregation phenomena

Inspired by a PDE-ODE system of aggregation developed in the biomathematical literature, an interacting particle system representing aggregation at the level of individuals is investigated. It is proved that the empirical density of the individual converges to solution of the PDE-ODE system.

math.PR↗

arXiv2018

The Navier-Stokes-Vlasov-Fokker-Planck system as a scaling limit of particles in a fluid

Convergence of a system of particles, interacting with a fluid, to Navier-Stokes-Vlasov-Fokker-Planck system is studied. The interaction between particles and fluid is described by Stokes drag force. The empirical measure of particles is proved to converge to the Vlasov-Fokker-Planck component of the system and the velocity of the fluid coupled with the particles converges in the uniform topology to the the Navier-Stokes component. A new uniqueness result for the PDE system is added.

math.PR↗

arXiv2018

The Vlasov-Navier-Stokes equations as a mean field limit

Convergence of particle systems to the Vlasov-Navier-Stokes equations is a difficult topic with only fragmentary results. Under a suitable modification of the classical Stokes drag force interaction, here a partial result in this direction is proven. A particle system is introduced, its interaction with the fluid is modelled and tightness is proved, in a suitable topology, for the family of laws of the pair composed by solution of Navier-Stokes equations and empirical measure of the particles. Moreover, it is proved that every limit law is supported on weak solutions of the Vlasov-Navier- Stokes system. Open problems, like weak-strong uniqueness for this system and its relevance for the convergence of the particle system, are outlined.

math.PR↗

arXiv2017

A mathematical model for growth of solid tumors and combination therapy with an application to colorectal cancer

We present a mathematical model, based on ordinary differential equations, for the evolution of solid tumors and their response to treatment. Specifically the effects of a cytotoxic agent and a monoclonal antibody are included as control term in the equations. The variables considered here are: the number of cancerous cells sensitive to chemotherapy, the number of cancerous cells resistant to chemotherapy, the degree of angiogenesis and the average intensity of VEGF. The rules that govern the quantities mentioned above are based on a geometrical argument: we approximate the tumor mass as a sphere and thus derive basic formulae for the normoxic cells and for VEGF production. The monoclonal antibody acts on VEGF and thus has in uence to the global degree of angiogenesis. Numerical estimates on some of the parameters are performed in order to match the main landmark in tumor progression and reaction to treatment in the specific case of colorectal cancer.

q-bio.TO↗