1,721,179 research outputs found
Small parameter limit for discrete-time, partially observed risk-sensitive control problems
No full textWe show that risk-sensitive control problems and deterministic dynamic games can be connected, under rather mild assumptions, by a small noise limit. In order to control this limit, new techniques are developed to study propagation of large deviations through conditional probabilities
Long time fluctuations at critical parameter of Hopf’s bifurcation
No full textA dynamical system that undergoes a supercritical Hopf’s bifurcation is perturbed by a
multiplicative Brownian motion that scales with a small parameter ε. The random fluctuations
of the system at the critical point are studied when the dynamics starts near equilibrium, in
the limit as ε goes to zero. Under a space–time scaling the system can be approximated by a
2-dimensional process lying on the center manifold of the Hopf’s bifurcation and a slow radial
component together with a fast angular component are identified. Then the critical fluctuations
are described by a ‘‘universal’’ stochastic differential equation whose coefficients are obtained
taking the average with respect to the fast variable
Heterogeneous credit portfolios and the dynamics of the aggregate losses.
No full textWe study the impact of contagion in a network of firms facing credit risk.We describe an intensity based model where the homogeneity assumption is broken by introducing a random environment that makes it possible to take into account the idiosyncratic characteristics of the firms. We shall see that our model goes
behind the identification of groups of firms that can be considered basically exchangeable. Despite this heterogeneity assumption our model has the advantage of being totally tractable. The aim is to quantify the losses that a bank may suffer in a large credit portfolio. Relying on a large deviation principle on the trajectory space of the process, we state a suitable law of large numbers and a central limit theorem useful for studying large portfolio losses. Simulation results are provided as well as applications to portfolio loss distribution analysis
Progetto di riconversione di due ospedali in strutture distrettuali per la realizzazione del sistema socio-sanitario dell'Alto Vicentino
No full textL’articolo presenta l’ipotesi con la quale, nell’ambito dell’Azienda sanitaria dell’Alto Vicentino, partendo dall’accorpamento dei due attuali ospedali in un’unica struttura in corso di costruzione, potrà essere riorganizzato l’intero sistema assistenziale, con la
creazione di una rete di servizi nella quale, da una parte, saranno attribuite al nuovo Ospedale e alle strutture distrettuali funzioni ben distinte ma tra loro coordinate, onde garantire al paziente la continuità delle cure dopo il ricovero ospedaliero; e, dall’altra, sarà assicurata una forte integrazione socio-sanitaria a livello distrettuale
A hierarchical mean field model of interacting spins
No full textWe consider a system of hierarchical interacting spins under dynamics of spin-flip type with a ferromagnetic mean field interaction, scaling with the hierarchical distance, coupled with a system of linearly interacting hierarchical diffusions of Ornstein-Uhlenbeck type. In particular, the diffusive variables enter in the spin-flip rates, effectively acting as dynamical magnetic fields. In absence of the diffusions, the spin-flip dynamics can be thought of as a modification of the Curie-Weiss model. We study the mean field and the two-level hierarchical model, in the latter case restricting to a subcritical regime, corresponding to high temperatures, obtaining macroscopic limits at different spatio-temporal scales and studying the phase transitions in the system. We also formulate a generalization of our results to the kth level hierarchical case, for any k finite, in the subcritical regime. We finally address the supercritical regime, in the zero-temperature limit, for the two-level hierarchical case, proceeding heuristically with the support of numerics. (C) 2021 Elsevier B.V. All rights reserved
McKean–Vlasov limit for interacting systems with simultaneous jumps
Full text linkMotivated by several applications, including neuronal models, we consider the McKean–Vlasov limit for a general class of mean-field systems of interacting diffusions characterized by an interaction via simultaneous jumps. We focus our interest on systems where the rate of the jumps is unbounded, which are rarely treated in the mean-field literature, and we prove well-posedness of the McKean–Vlasov limit together with propagation of chaos via a coupling technique. To highlight the role of simultaneous jumps, we introduce an intermediate process which is close to the original particle system but does not display simultaneous jumps. This shows in particular that the simultaneous jumps contribute to the overall rate of convergence of the N-particle empirical measures by a term of order 1/√N
Oscillatory Behavior in a Model of Non-Markovian Mean Field Interacting Spins
Full text linkWe analyze a non-Markovian mean field interacting spin system, related to the Curie–Weiss model. We relax the Markovianity assumption by replacing the memoryless distribution of the waiting times of a classical spin-flip dynamics with a distribution with memory. The resulting stochastic evolution for a single particle is a spin-valued renewal process, an example of a two-state semi-Markov process. We associate to the individual dynamics an equivalent Markovian description, which is the subject of our analysis. We study a corresponding interacting particle system, where a mean field interaction-depending on the magnetization of the system-is introduced as a time scaling on the waiting times between two successive particle’s jumps. Via linearization arguments on the Fokker–Planck mean field limit equation, we give evidence of emerging periodic behavior. Specifically, numerical analysis on the discrete spectrum of the linearized operator, characterized by the zeros of an explicit holomorphic function, suggests the presence of a Hopf bifurcation for a critical value of the temperature. The presence of a Hopf bifurcation in the limit equation matches the emergence of a periodic behavior obtained by simulating the N-particle system
A hierarchical mean field model of interacting spins
No full textWe consider a system of hierarchical interacting spins under dynamics of spin-flip type with a ferromagnetic mean field interaction, scaling with the hierarchical distance, coupled with a system of linearly interacting hierarchical diffusions of Ornstein–Uhlenbeck type. In particular, the diffusive variables enter in the spin-flip rates, effectively acting as dynamical magnetic fields. In absence of the diffusions, the spin-flip dynamics can be thought of as a modification of the Curie–Weiss model. We study the mean field and the two-level hierarchical model, in the latter case restricting to a subcritical regime, corresponding to high temperatures, obtaining macroscopic limits at different spatio-temporal scales and studying the phase transitions in the system. We also formulate a generalization of our results to the kth level hierarchical case, for any k finite, in the subcritical regime. We finally address the supercritical regime, in the zero-temperature limit, for the two-level hierarchical case, proceeding heuristically with the support of numerics
- …
