Oblique derivative problems and invariant measures
On a gambler's ruin problem
On a generalization of a theorem of W. Sudderth and some applications
On a generalization of the martingale maximal theorem
On a non-linear semi-group associated with stochastic optimal control and its excessive majorant
On a stopped brownian motion formula of H. M. Taylor
On almost sure convergence without the Radon-Nikodym property.
On complete convergence of the sum of a random number of stable type random elements.
On Expectation of the Maximum for Sums of Independent Random Variables.
On impulsive control with long run average cost criterion
On independent times and positions for Brownian motions.
On infinite horizon multi-person stopping games with priorities
We study nonzero-sum multi-person multiple stopping games with players' priorities. The existence of Nash equilibrium is proved. Examples of multi stopping of Markov chains are considered. The game may also be presented as a special case of a stochastic game which leads to many variations of it, in which stopping is a part of players' strategies.
On non-ergodic versions of limit theorems
The author investigates non ergodic versions of several well known limit theorems for strictly stationary processes. In some cases, the assumptions which are given with respect to general invariant measure, guarantee the validity of the theorem with respect to ergodic components of the measure. In other cases, the limit theorem can fail for all ergodic components, while for the original invariant measure it holds.
On optimal stopping of inhomogeneous standard Markov processes.
On randomized stopping times.
In this note we give a proof of the fact that the extremal elements of the set of randomized stopping times are exactly the stopping times.
On sequential plans for the exponential class of processes
On Skorohod embedding in -dimensional brownian motion by means of natural stopping times
On the Azéma-Yor stopping time
On the Barlow-Yor inequalities for local time
On the exponential Orlicz norms of stopped Brownian motion
Necessary and sufficient conditions are found for the exponential Orlicz norm (generated by with 0 < p ≤ 2) of or to be finite, where is a standard Brownian motion and τ is a stopping time for B. The conditions are in terms of the moments of the stopping time τ. For instance, we find that as soon as for some constant C > 0 as k → ∞ (or equivalently ). In particular, if τ ∼ Exp(λ) or then the last condition is satisfied, and we obtain with some universal constant K > 0....