We study pathwise properties and homeomorphic property with respect to the initial values for stochastic differential equations driven by G-Brownian motion. We first present a Burkholder-Davis-Gundy inequality and an extension of Itô's formula for the G-stochastic integrals. Some moment...

Fractional diffusion equations of order [nu][set membership, variant](0,2) are examined and solved under different types of boundary conditions. In particular, for the fractional equation on the half-line [0,+[infinity]) and with an elastic boundary condition at x=0, we are able to provide the...

We consider the Skorokhod problem in a time-varying interval. We prove existence and uniqueness of the solution. We also express the solution in terms of an explicit formula. Moving boundaries may generate singularities when they touch. Under the assumption that the first time [tau] when the...

We study the Gibbsian character of time-evolved planar rotor systems (that is, systems which have two-component, classical XY, spins) on , d=2, in the transient regime, evolving with stochastic dynamics and starting from an initial Gibbs measure [nu]. We model the system with interacting...

A crucial property for dynamic risk measures is the time consistency. In this paper, a characterization of time consistency in terms of a "cocycle condition" for the minimal penalty function is proved for general dynamic risk measures continuous from above. Then the question of the regularity of...

One of the main objectives of equilibrium state statistical physics is to analyze which symmetries of an interacting particle system in equilibrium are broken or conserved. Here we present a general result on the conservation of translational symmetry for two-dimensional Gibbsian particle...

We consider an optimal reinsurance strategy in which the insurance company (1) monitors the dynamics of its surplus process, (2) optimally chooses a time to begin negotiating with a reinsurer to buy quota-share, or proportional, reinsurance, which introduces an implementation delay (denoted by...

We study finite horizon optimal switching problems for hidden Markov chain models with point process observations. The controller possesses a finite range of strategies and attempts to track the state of the unobserved state variable using Bayesian updates over the discrete observations. Such a...

The so-called swapping algorithm was designed to simulate from spin glass distributions, among others. In this note we show that it mixes rapidly, in a very simple disordered system, the Hopfield model with two patterns.

We study a new class of ergodic backward stochastic differential equations (EBSDEs for short) which is linked with semi-linear Neumann type boundary value problems related to ergodic phenomena. The particularity of these problems is that the ergodic constant appears in Neumann boundary...