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Maria João Oliveira

Publications and source records attributed to Maria João Oliveira.

9 recordsLinked to original sources
arXiv2023

Hydrodynamic limits for the free Kawasaki dynamics of continuous particle systems

An infinite particle system of independent jumping particles in infinite volume is considered. Their construction is recalled,further properties are derived, the relation with hierarchical equations, Poissonian analysis, and second quantization are discussed. The hydrodynamic limit for a general initial distribution satisfying a mixing condition is derived. The long time asymptotic is computed under an extra assumption. The relation with constructions based on infinite volume limits is discussed.

math.PR↗
arXiv2011

Glauber dynamics in the continuum via generating functionals evolution

We construct the time evolution for states of Glauber dynamics for a spatial infinite particle system in terms of generating functionals. This is carried out by an Ovsjannikov-type result in a scale of Banach spaces, leading to a local (in time) solution which, under certain initial conditions, might be extended to a global one. An application of this approach to Vlasov-type scaling in terms of generating functionals is considered as well.

math-ph↗
arXiv2010

The fractional volatility model: No-arbitrage, leverage and risk measures

Based on a criterium of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions of the model are obtained with different leverage behavior. Here, the no-arbitrage and incompleteness properties of the model are studied. Some risk measures are also discussed in this framework.

q-fin.PR↗
arXiv2003

Invariant measures for Glauber dynamics of continuous systems

We consider Glauber-type stochastic dynamics of continuous systems \cite{BCC02}, \cite{KL03}, a particular case of spatial birth-and-death processes. The dynamics is defined by a Markov generator in such a way that Gibbs measures of Ruelle type are symmetrizing, and hence invariant for the stochastic dynamics. In this work we show that the converse statement is also true. Namely, all invariant measures satisfying Ruelle bound condition are grand canonical Gibbsian for the potential defining the dynamics. The proof is based on the observation that the well-known Kirkwood-Salsburg equation for correlation functions is indeed an equilibrium equation for the stochastic dynamics.

math-ph↗