On semi-martingale characterizations of functionals of symmetric Markov processes.
On semi-martingales associated with crossings
On sequences of σ-algebras
On sequential plans for the exponential class of processes
On sequentially weakly Feller solutions to SPDE’s
A rather general class of stochastic evolution equations in Hilbert spaces whose transition semigroups are Feller with respect to the weak topology is found, and consequences for existence of invariant measures are discussed.
On set covariance and three-point test sets
The information contained in the measure of all shifts of two or three given points contained in an observed compact subset of is studied. In particular, the connection of the first order directional derivatives of the described characteristic with the oriented and the unoriented normal measure of a set representable as a finite union of sets with positive reach is established. For smooth convex bodies with positive curvatures, the second and the third order directional derivatives of the characteristic...
On Sets of Integers with Prescribed Gaps.
On Shannon-McMillan's limit theorem for pairs of stationary random processes
On sharp Burkholder–Rosenthal-type inequalities for infinite-degree U-statistics
On shifted convolution powers of a probility measure.
On shifting iterated convolutions I
On simulation of multidimensional random sequences
On singular integrals with respect to the gaussian measure
On Skorohod embedding in -dimensional brownian motion by means of natural stopping times
On small deviation probabilities of positive random variables.
On small deviations of Gaussian processes using majorizing measures
We give two examples of periodic Gaussian processes, having entropy numbers of exactly the same order but radically different small deviations. Our construction is based on Knopp's classical result yielding existence of continuous nowhere differentiable functions, and more precisely on Loud's functions. We also obtain a general lower bound for small deviations using the majorizing measure method. We show by examples that our bound is sharp. We also apply it to Gaussian independent sequences and...
On small solutions of second order differential equations with random coefficients
We consider the equation where is a given increasing sequence of positive numbers, and is chosen at random so that are totally independent random variables uniformly distributed on interval . We determine the probability of the event that all solutions of the equation tend to zero as .
On small stochastic perturbations of mappings of the unit interval
On smoothing properties of transition semigroups associated to a class of SDEs with jumps
We prove smoothing properties of nonlocal transition semigroups associated to a class of stochastic differential equations (SDE) in driven by additive pure-jump Lévy noise. In particular, we assume that the Lévy process driving the SDE is the sum of a subordinated Wiener process (i.e. , where is an increasing pure-jump Lévy process starting at zero and independent of the Wiener process ) and of an arbitrary Lévy process independent of , that the drift coefficient is continuous (but not...
On solutions of general nonlinear stochastic integral equations.