On a Berry-Esseen type bound for the maximum likelihood estimator of a parameter for some stochastic partial differential equations.
On a strongly consistent estimator of the squared L_2-norm of a function
A kernel estimator of the squared -norm of the intensity function of a Poisson random field is defined. It is proved that the estimator is asymptotically unbiased and strongly consistent. The problem of estimating the squared -norm of a function disturbed by a Wiener random field is also considered.
On conditional independence and log-convexity
If conditional independence constraints define a family of positive distributions that is log-convex then this family turns out to be a Markov model over an undirected graph. This is proved for the distributions on products of finite sets and for the regular Gaussian ones. As a consequence, the assertion known as Brook factorization theorem, Hammersley–Clifford theorem or Gibbs–Markov equivalence is obtained.
On estimation in random fields generated by linear stochastic partial differential equations
On Optimal Allocations for Estimating the Surface of a Random Field.
On the approximation of some optimal sequential plan
On the concept of the asymptotic Rényi distances for random fields
The asymptotic Rényi distances are explicitly defined and rigorously studied for a convenient class of Gibbs random fields, which are introduced as a natural infinite-dimensional generalization of exponential distributions.