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Large population limit and time behaviour of a stochastic particle model describing an age-structured population

Viet Chi Tran (2008)

ESAIM: Probability and Statistics

 We study a continuous-time discrete population structured by a vector of ages. Individuals reproduce asexually, age and die. The death rate takes interactions into account. Adapting the approach of Fournier and Méléard, we show that in a large population limit, the microscopic process converges to the measure-valued solution of an equation that generalizes the McKendrick-Von Foerster and Gurtin-McCamy PDEs in demography. The large deviations associated with this convergence are studied. The upper-bound...

Local volatility in the Heston model: a Malliavin calculus approach.

Ewald, Christian-Oliver (2005)

Journal of Applied Mathematics and Stochastic Analysis

Localization of spectrum bottom for the Stokes operator in a random porous medium.

Yurinsky, V.V. (2001)

Siberian Mathematical Journal

Log-optimal investment in the long run with proportional transaction costs when using shadow prices

Petr Dostál, Jana Klůjová (2015)

Kybernetika

We consider a non-consuming agent interested in the maximization of the long-run growth rate of a wealth process investing either in a money market and in one risky asset following a geometric Brownian motion or in futures following an arithmetic Brownian motion. The agent faces proportional transaction costs, and similarly as in [17] where the case of stock trading is considered, we show how the log-optimal optimal policies in the long run can be derived when using the technical tool of shadow...

Low-variance direct Monte Carlo simulations using importance weights

Husain A. Al-Mohssen, Nicolas G. Hadjiconstantinou (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present an efficient approach for reducing the statistical uncertainty associated with direct Monte Carlo simulations of the Boltzmann equation. As with previous variance-reduction approaches, the resulting relative statistical uncertainty in hydrodynamic quantities (statistical uncertainty normalized by the characteristic value of quantity of interest) is small and independent of the magnitude of the deviation from equilibrium, making the simulation of arbitrarily small deviations from equilibrium possible....