On Lévy's downcrossing theorem and various extensions
On limit properties of the reward from a Markov replacement process
On local times of a diffusion
On long time almost sure asymptotics of renormalized branching diffusion processes
On Markovian cocycle perturbations in classical and quantum probability.
On Markovian decision processes with unbounded rewards
On Markovian traffic with applications to TES processes.
On maximum increase and decrease of brownian motion
On modelling long term stock returns with ergodic diffusion processes: arbitrage and arbitrage-free specifications.
On moments for branching processes
On nearly selfoptimizing strategies for multiarmed bandit problems with controlled arms
Two kinds of strategies for a multiarmed Markov bandit problem with controlled arms are considered: a strategy with forcing and a strategy with randomization. The choice of arm and control function in both cases is based on the current value of the average cost per unit time functional. Some simulation results are also presented.
On near-optimal necessary and sufficient conditions for forward-backward stochastic systems with jumps, with applications to finance
We establish necessary and sufficient conditions of near-optimality for nonlinear systems governed by forward-backward stochastic differential equations with controlled jump processes (FBSDEJs in short). The set of controls under consideration is necessarily convex. The proof of our result is based on Ekeland's variational principle and continuity in some sense of the state and adjoint processes with respect to the control variable. We prove that under an additional hypothesis, the near-maximum...
On nodal lines of Neumann eigenfunctions.
On Nonuniform Gaussian Approximation for Random Summation.
On optimal replacement policy
A system with a single activated unit which can be in states is considered. Inspections of the system are carried out at discrete time instants. The process of deterioration of the unit is supposed to be Markovian. The unit by its operation brings an income which is monotonically dependent on its state. A replacement of the unit is associated with certain costs. The paper gives an effective algorithm for finding the replacement strategy maximizing the average income of the system per unit time....
On optimal stopping of inhomogeneous standard Markov processes.
On pathwise uniqueness for stochastic differential equations driven by stable Lévy processes
We study a one-dimensional stochastic differential equation driven by a stable Lévy process of order with drift and diffusion coefficients , . When , we investigate pathwise uniqueness for this equation. When , we study another stochastic differential equation, which is equivalent in law, but for which pathwise uniqueness holds under much weaker conditions. We obtain various results, depending on whether or and on whether the driving stable process is symmetric or not. Our assumptions...
On perturbations of strongly admissible prior distributions
On (r, 2)-capacities for a class of elliptic pseudo differential operators.
On random evolutions induced by countable state space Markov chains