State dependent multitype spatial branching processes and their longtime behavior.
Stationary distributions for jump processes with memory
We analyze a jump processes with a jump measure determined by a “memory” process . The state space of is the Cartesian product of the unit circle and the real line. We prove that the stationary distribution of is the product of the uniform probability measure and a Gaussian distribution.
Stationary Markov sets
Stationary measures and phase transition for a class of probabilistic cellular automata
We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models.
Stationary measures and phase transition for a class of Probabilistic Cellular Automata
We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models.
Stationary Quantum Markov processes as solutions of stochastic differential equations
From the operator algebraic approach to stationary (quantum) Markov processes there has emerged an axiomatic definition of quantum white noise. The role of Brownian motion is played by an additive cocycle with respect to its time evolution. In this report we describe some recent work, showing that this general structure already allows a rich theory of stochastic integration and stochastic differential equations. In particular, if a quantum Markov process is represented by a unitary cocycle, we can...
Stationary random graphs with prescribed iid degrees on a spatial Poisson process.
Stationary solutions and forward equations for controlled and singular martingale problems.
Stationary solutions for heat equation perturbed by general additive noise.
Statistical Modelling: Application to the financial sector
Our research is centred on the stochastic structure of matched open populations, subjected to periodical reclassifications. These populations are divided into sub-populations. In our application we considered two populations of customers of a bank: with and without account manager. Two or more of such population are matched when there is a 1-1 correspondence between their sub-populations and the elements of one of them can go to another, if and only if the same occurs with elements from the...
Statistical models for analysing criminal careers
Statistiques de diffusions et temps local
Steady state and scaling limit for a traffic congestion model
In a general model (AIMD) of transmission control protocol (TCP) used in internet traffic congestion management, the time dependent data flow vector x(t) > 0 undergoes a biased random walk on two distinct scales. The amount of data of each component xi(t) goes up to xi(t)+a with probability 1-ζi(x) on a unit scale or down to γxi(t), 0 < γ < 1 with probability ζi(x) on a logarithmic scale, where ζi depends on the joint state of the system x. We investigate the long time behavior, mean field...
Steady-state distributions of piecewise Markov processes
Stochastic algorithm for Bayesian mixture effect template estimation
The estimation of probabilistic deformable template models in computer vision or of probabilistic atlases in Computational Anatomy are core issues in both fields. A first coherent statistical framework where the geometrical variability is modelled as a hidden random variable has been given by [S. Allassonnière et al., J. Roy. Stat. Soc.69 (2007) 3–29]. They introduce a Bayesian approach and mixture of them to estimate deformable template models. A consistent stochastic algorithm has been introduced...
Stochastic analysis and local times for (N, d)-Wiener process
Stochastic approach to the process of red cell destruction
Stochastic calculus and degenerate boundary value problems
Consider the boundary value problem (L.P): in , on where is written as , and is a general Venttsel’s condition (including the oblique derivative condition). We prove existence, uniqueness and smoothness of the solution of (L.P) under the Hörmander’s condition on the Lie brackets of the vector fields (), for regular open sets with a non-characteristic boundary.Our study lies on the stochastic representation of and uses the stochastic calculus of variations for the -diffusion process...
Stochastic calculus and the continuity of local times of Lévy processes
Stochastic characterization of plurisubharmonicity and convexity of functions
It is described how both plurisubharmonicity and convexity of functions can be characterized in terms of simple to work with classes of holomorphic martingales, namely a class of driftless Itô processes satisfying a skew-symmetry property and a family of linear modifications of Brownian motion parametrized by a compact set.