Marches de Harris sur les groupes localement compacts. II
The invariant measures for a Markovian operator corresponding to a random walk, in a random stationary one-dimensional environment defined by a dynamical system, are quasi-invariant measures for the system. We discuss the construction of such measures in the general case and show unicity, under some assumptions, for a rotation on the circle.
A solution to the marginal problem is obtained in a form of parametric exponential (Gibbs–Markov) distribution, where the unknown parameters are obtained by an optimization procedure that agrees with the maximum likelihood (ML) estimate. With respect to a difficult performance of the method we propose also an alternative approach, providing the original basis of marginals can be appropriately extended. Then the (numerically feasible) solution can be obtained either by the maximum pseudo-likelihood...
Quantum trajectories are solutions of stochastic differential equations obtained when describing the random phenomena associated to quantum continuous measurement of open quantum system. These equations, also called Belavkin equations or Stochastic Master equations, are usually of two different types: diffusive and of Poisson-type. In this article, we consider more advanced models in which jump–diffusion equations appear. These equations are obtained as a continuous time limit of martingale problems...
Martingale Hardy spaces and BMO spaces generated by an operator T are investigated. An atomic decomposition of the space is given if the operator T is predictable. We generalize the John-Nirenberg theorem, namely, we prove that the spaces generated by an operator T are all equivalent. The sharp operator is also considered and it is verified that the norm of the sharp operator is equivalent to the norm. The interpolation spaces between the Hardy and BMO spaces are identified by the real method....