On a class of processes with multiplicity .
On a construction of majorizing measures on subsets of ℝⁿ with special metrics
We consider processes Xₜ with values in and “time” index t in a subset A of the unit cube. A natural condition of boundedness of increments is assumed. We give a full characterization of the domains A for which all such processes are a.e. continuous. We use the notion of Talagrand’s majorizing measure as well as geometrical Paszkiewicz-type characteristics of the set A. A majorizing measure is constructed.
On certain almost brownian filtrations
On certain probabilities equivalent to Wiener measure, d'après Dubins, Feldman, Smorodinsky and Tsirelson
On convex stochastic processes.
On countable dense random sets
On Markovian traffic with applications to TES processes.
On Paszkiewicz-type criterion for a.e. continuity of processes in -spaces
In this paper we consider processes Xₜ with values in , p ≥ 1 on subsets T of a unit cube in ℝⁿ satisfying a natural condition of boundedness of increments, i.e. a process has bounded increments if for some non-decreasing f: ℝ₊ → ℝ₊ ||Xₜ-Xₛ||ₚ ≤ f(||t-s||), s,t ∈ T. We give a sufficient criterion for a.s. continuity of all processes with bounded increments on subsets of a given set T. This criterion turns out to be necessary for a wide class of functions f. We use a geometrical Paszkiewicz-type...
On some properties of J-convex stochastic processes.
On the Ray topology
On Vershik's standardness criterion and Tsirelson's notion of cosiness
Optional splitting formula in a progressively enlarged filtration
Let F be a filtration andτbe a random time. Let G be the progressive enlargement of F withτ. We study the following formula, called the optional splitting formula: For any G-optional processY, there exists an F-optional processY′ and a function Y′′ defined on [0,∞] × (ℝ+ × Ω) being ℬ[0,∞]⊗x1d4aa;(F) measurable, such that Y=Y′1[0,τ)+Y′′(τ)1[τ,∞). (This formula can also be formulated for multiple random timesτ1,...,τk). We are interested in this formula because of its fundamental role in many...