A note on the tail accuracy of the univariate saddlepoint approximation
A note on the two-sided regulated random walk
A note on the upper bounds for the dispersion.
A note on the weak convergence of probability measures on
A note on weak convergence on martingale measures
A note on weak solutions to stochastic differential equations
We revisit the proof of existence of weak solutions of stochastic differential equations with continuous coeficients. In standard proofs, the coefficients are approximated by more regular ones and it is necessary to prove that: i) the laws of solutions of approximating equations form a tight set of measures on the paths space, ii) its cluster points are laws of solutions of the limit equation. We aim at showing that both steps may be done in a particularly simple and elementary manner.
A note on γ-radonifying and summing operators
In this note, we discuss certain generalizations of γ-radonifying operators and their applications to the regularity for linear stochastic evolution equations on some special Banach spaces. Furthermore, we also consider a more general class of operators, namely the so-called summing operators and discuss the application to the compactness of the heat semi-group between weighted -spaces.
A note to paper “On the stability of cubic mappings and quartic mappings in random normed spaces”.
A novel robust principal component analysis method for image and video processing
The research on the robust principal component analysis has been attracting much attention recently. Generally, the model assumes sparse noise and characterizes the error term by the -norm. However, the sparse noise has clustering effect in practice so using a certain -norm simply is not appropriate for modeling. In this paper, we propose a novel method based on sparse Bayesian learning principles and Markov random fields. The method is proved to be very effective for low-rank matrix recovery...
A numerical constant associated with generalized convolutions
A -adic study of the partial sums of the harmonic series.
A Paley type inequality for two-parameter Vilenkin-Fourier coefficients.
A paradox in a queueing network with state-dependent routing and loss.
A pathwise solution for nonlinear parabolic equations with stochastic perturbations
We analyse here a semilinear stochastic partial differential equation of parabolic type where the diffusion vector fields are depending on both the unknown function and its gradient ∂ xu with respect to the state variable, ∈ ℝn. A local solution is constructed by reducing the original equation to a nonlinear parabolic one without stochastic perturbations and it is based on a finite dimensional Lie algebra generated by the given diffusion vector fields.
A PDE approach to certain large deviation problems for systems of parabolic equations
A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities
A penalized bandit algorithm.
A percolation formula.
A Pettis-type integral and applications to transition semigroups
Motivated by applications to transition semigroups, we introduce the notion of a norming dual pair and study a Pettis-type integral on such pairs. In particular, we establish a sufficient condition for integrability. We also introduce and study a class of semigroups on such dual pairs which are an abstract version of transition semigroups. Using our results, we give conditions ensuring that a semigroup consisting of kernel operators has a Laplace transform which also consists of kernel operators....
A philatelic excursion with Jeff Hunter in probability and matrix theory.