A characterization of the set of fixed points of the quicksort transformation.
A characterization of the weak convergence of convolution powers
A Characterization of Uniform Distribution
Is the Lebesgue measure on [0,1]² a unique product measure on [0,1]² which is transformed again into a product measure on [0,1]² by the mapping ψ(x,y) = (x,(x+y)mod 1))? Here a somewhat stronger version of this problem in a probabilistic framework is answered. It is shown that for independent and identically distributed random variables X and Y constancy of the conditional expectations of X+Y-I(X+Y > 1) and its square given X identifies uniform distribution either absolutely continuous or discrete....
A characterization of α-convolutions
A Characterization using the Conditional Variance.
A Ciesielski–Taylor type identity for positive self-similar Markov processes
The aim of this note is to give a straightforward proof of a general version of the Ciesielski–Taylor identity for positive self-similar Markov processes of the spectrally negative type which umbrellas all previously known Ciesielski–Taylor identities within the latter class. The approach makes use of three fundamental features. Firstly, a new transformation which maps a subset of the family of Laplace exponents of spectrally negative Lévy processes into itself. Secondly, some classical features...
A clark-ocone formula in UMD Banach spaces.
A class of Compound Poisson Distribution and its Stochastic Dervations
A Class of Contractions in Hilbert Space and Applications
We characterize the bounded linear operators T in Hilbert space which satisfy T = βI + (1-β)S where β ∈ (0,1) and S is a contraction. The characterizations include a quadratic form inequality, and a domination condition of the discrete semigroup by the continuous semigroup . Moreover, we give a stronger quadratic form inequality which ensures that . The results apply to large classes of Markov operators on countable spaces or on locally compact groups.
A class of Feller semigroups generated by pseudo differential operators.
A class of nonstationary adic transformations
A class of quasigroups solving a problem of ergodic theory
A pointed quasigroup is said to be semicentral if it is principally isotopic to a group via a permutation on one side and a group automorphism on the other. Convex combinations of permutation matrices given by the one-sided multiplications in a semicentral quasigroup then yield doubly stochastic transition matrices of finite Markov chains in which the entropic behaviour at any time is independent of the initial state.
A class of strong limit theorems for countable nonhomogeneous Markov chains on the generalized gambling system
In this paper, we study the limit properties of countable nonhomogeneous Markov chains in the generalized gambling system by means of constructing compatible distributions and martingales. By allowing random selection functions to take values in arbitrary intervals, the concept of random selection is generalized. As corollaries, some strong limit theorems and the asymptotic equipartition property (AEP) theorems for countable nonhomogeneous Markov chains in the generalized gambling system are established....
A combinatorial approach to the conditioning of a single entry in the stationary distribution for a Markov chain.
A combinatorial derivation of the PASEP stationary state.
A combinatorial problem arising in finite Markov chains
A comparison of algorithms to filter noisy observations of a linear differential system driven by Brownian motion and a simple Markov switching process
A comparison of approaches for the construction of reduced basis for stochastic Galerkin matrix equations
We examine different approaches to an efficient solution of the stochastic Galerkin (SG) matrix equations coming from the Darcy flow problem with different, uncertain coefficients in apriori known subdomains. The solution of the SG system of equations is usually a very challenging task. A relatively new approach to the solution of the SG matrix equations is the reduced basis (RB) solver, which looks for a low-rank representation of the solution. The construction of the RB is usually done iteratively...
A comparison of deterministic and Bayesian inverse with application in micromechanics
The paper deals with formulation and numerical solution of problems of identification of material parameters for continuum mechanics problems in domains with heterogeneous microstructure. Due to a restricted number of measurements of quantities related to physical processes, we assume additional information about the microstructure geometry provided by CT scan or similar analysis. The inverse problems use output least squares cost functionals with values obtained from averages of state problem quantities...
A comparison theorem for semimartingales and its applications