On pathwise uniqueness and expansion of filtrations
On pathwise uniqueness for stochastic differential equations driven by stable Lévy processes
We study a one-dimensional stochastic differential equation driven by a stable Lévy process of order with drift and diffusion coefficients , . When , we investigate pathwise uniqueness for this equation. When , we study another stochastic differential equation, which is equivalent in law, but for which pathwise uniqueness holds under much weaker conditions. We obtain various results, depending on whether or and on whether the driving stable process is symmetric or not. Our assumptions...
On pendant vertices in random graphs
On percolation in random graphs with given vertex degrees.
On perturbations of strongly admissible prior distributions
On Poisson and composed Poisson stochastic set functions
On Poisson-Dirichlet problems with polynomial data
In this note we provide a probabilistic proof that Poisson and/or Dirichlet problems in an ellipsoid in Rd, that have polynomial data, also have polynomial solutions. Our proofs use basic stochastic calculus. The existing proofs are based on famous lemma by E. Fisher which we do not use, and present a simple martingale proof of it as well.
On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications
On practical problems with the explanation of the difference between possibility and probability
On preservation under univariate weighted distributions
We derive some new results for preservation of various stochastic orders and aging classes under weighted distributions. The corresponding reversed preservation properties as straightforward conclusions of the obtained results for the direct preservation properties, are developed. Damage model of Rao, residual lifetime distribution, proportional hazards and proportional reversed hazards models are discussed as special weighted distributions to try some of our results.
On probabilities in certain multivariate distributions: their dependence on correlations
On Probability Distribution Solutions of a Functional Equation
Let 0 < β < α < 1 and let p ∈ (0,1). We consider the functional equation φ(x) = pφ (x-β)/(1-β) + (1-p)φ(minx/α, (x(α-β)+β(1-α))/α(1-β)) and its solutions in two classes of functions, namely ℐ = φ: ℝ → ℝ|φ is increasing, , , = φ: ℝ → ℝ|φ is continuous, , . We prove that the above equation has at most one solution in and that for some parameters α,β and p such a solution exists, and for some it does not. We also determine all solutions of the equation in ℐ and we show the exact connection...
On Probability Function On Pseudo-Boolean Algebra
On probability generating functions for matching and occupancy distributions
On probability of first order formulas in a given model
On processes with conditional independent increments and stable convergence in law
On products of admissible liftings and densities.
On Prohorov spaces
On properties of binary random numbers
On pseudo-random sequences and their relation to a class of stochastical laws