1,721,276 research outputs found
Space-time large deviations for interacting particle systems
No full textWe prove a process-level large deviation principle for the space-time empirical averages of continuous-time systems on an infinite lattice. Our methods rely on the Donsker-Varadhan large deviation theory for Markov processes, and allow us to express the rate function rather explicitly in terms of the Markov generator of the infinite particle system. We can prove our principle for a large class of spin systems with no particle exchange, as well as for infinite diffusion processes whose drift is the gradient of a finite range Hamiltonian
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
Logarithmic Sobolev Inequality for Zero-Range Dynamics: independence of the particle number
No full textWe prove that the logarithmic-Sobolev constant for Zero-Range Processes in a box of diameter L may depend on L but not on the number of particles. This is a first, but relevant and quite technical step, in the proof that this logarithmic-Sobolev constant grows as the square of L, that is presented in a forthcoming paper
Logarithmic Sobolev inequality for zero range dynamics
No full textWe consider a system of interacting particles on a finite subset of diameter L of the d-dimensional integer lattice, and with zero-range interaction. Under mild technical conditions, we prove that the logarithmic-Sobolev constant grows as L^
Large deviations and stationary measures for interacting particle systems
No full textVarious properties of the rate function of a large deviation principle for the space-time empirical process of an interacting particle system are studied here. In particular we show that the minimum points of the rate function correspond to the stationary measures for the system
Stochastic Mean-Field Dynamics and Applications to Life Sciences
No full textAlthough we do not intend to give a general, formal definition, the stochastic mean-field dynamics we present in these notes can be conceived as the random evolution of a system comprised by N interacting components which is: (a) invariant in law for permutation of the components; (b) such that the contribution of each component to the evolution of any other is of order 1 1 N . The permutation invariance clearly does not allow any freedom in the choice of the geometry of the interaction; however, this is exactly the feature that makes these models analytically treatable, and therefore attractive for a wide scientific community
Detecting nonergodicity in continuous-time spin systems
No full textWe develop an empirical test aimed at detecting nonergodicity from a single sample of a spin system. We show that the test is asymptotically correct, and we give explicit asymptotics for the error probability. The key tool consists in some new large-deviation estimates
First occurrence time of a large density fluctuation for a system of independent random walks
Full text linkWe obtain sharp asymptotics for the firsttimea “macroscopic” densityfluctuation occurs in asystem of independent simple symmetric randomwalks on Zd. Also, we show the convergence of the moments of the rescaled time by establishing tail estimates
Quasi-stationary measures for conservative dynamics in the infinite lattice
Full text linkWe study quasi-stationary measures for conservative particle systems
in the infinite lattice. Existence of quasi-stationary measures is established
for a fairly general class of reversible systems. For the special cases of a
system of independent random walks and the symmetric simple exclusion
process, it is shown that qualitative features of quasi-stationary measures
change drastically with dimension
A stochastic control approach to reciprocal diffusion processes
No full textThe problem of forcing a nondegenerate diffusion process to a given final configuration is considered. Using the logarithmic transformation approach developed by Fleming, it is shown that the perturbation of the drift suggested by Jamison solves an optimal stochastic control problem. Such perturbation happens to have minimum energy between all controls that bring the diffusion to the desired final distribution. A special property of the change of measure on the path-space that corresponds to the aforesaid perturbation of the drift is also shown
- …
