The Poisson Boundary of Polycyclic Groups
The Poisson boundary of random rational affinities
We prove that in order to describe the Poisson boundary of rational affinities, it is necessary and sufficient to consider the action on real and all -adic fileds.
The Poisson formula for groups with hyperbolic properties.
The Pólya characterization of a Gaussian measure on groups
The Pólya-Aeppli process and ruin problems.
The posterior metric and the goodness of gibbsianness for transforms of Gibbs measures.
The Powers sum of spatial CPD-semigroups and CP-semigroups
We define spatial CPD-semigroups and construct their Powers sum. We construct the Powers sum for general spatial CP-semigroups. In both cases, we show that the product system of that Powers sum is the product of the spatial product systems of its factors. We show that on the domain of intersection, pointwise bounded CPD-semigroups on the one side and Schur CP-semigroups on the other, the constructions coincide. This summarizes all known results about Powers sums and generalizes them considerably....
The present and future of signal processing
The pricing of credit risky securities under stochastic interest rate model with default correlation
In this paper, we study the pricing of credit risky securities under a three-firms contagion model. The interacting default intensities not only depend on the defaults of other firms in the system, but also depend on the default-free interest rate which follows jump diffusion stochastic differential equation, which extends the previous three-firms models (see R. A. Jarrow and F. Yu (2001), S. Y. Leung and Y. K. Kwok (2005), A. Wang and Z. Ye (2011)). By using the method of change of measure and...
The principle of large deviations for martingale additive functionals of recurrent Markov processes.
The principle of truncations in applied probability
The principle of variation for relativistic quantum particles
The probabilistic approach to the analysis of the limiting behavior of an integro-differential equation depending on a small parameter, and its application to stochastic processes.
The Probabilistic Solution of the Dirichlet Problem for Degenerate Elliptic Equations
We study the Dirichlet problem for degenerate elliptic equations, and show that the probabilistic solution is a unique viscosity solution.
The probability of a successful allocation of ball groups by boxes.
The probability of large deviations for the sum functions of spacings.
The probability of the triangle inequality in probabilistic metric squares.
The probability that brownian motion almost contains a line
The problem of points before Pascal. (Le problème des partis avant Pascal.)