A biased roulette
A bound on the moment generating function of a sum of dependent variables with an application to simple random sampling without replacement
A continuous-time search model with finite horizon
A controller and a stopper game with degenerate variance control.
A game model referring to the control of independent discrete time stochastic processes
A generalized Chacon's inequality and order convergence of processes
A generalized fundamental identity
A non-linear Riesz respresentation in probabilistic potential theory
A non-Markovian process with unbounded -variation.
A note on a selection problem
A note on 'Big Match'
We present a very simple proof of the existence of the value for 'Big Match' first shown by Blackwell and Ferguson (1968).
A note on “Big-Match”
A note on dilations and martingales.
A note on exponentially bounded stopping times of certain one-sample sequential rank order tests.
A recurrence theorem for square-integrable martingales
Let be a zero-mean martingale with canonical filtration and stochastically -bounded increments which means that a.s. for all n ≥ 1, t > 0 and some square-integrable distribution H on [0,∞). Let . It is the main result of this paper that each such martingale is a.s. convergent on V < ∞ and recurrent on V = ∞, i.e. for some c > 0. This generalizes a recent result by Durrett, Kesten and Lawler [4] who consider the case of only finitely many square-integrable increment distributions....
A second order SDE for the Langevin process reflected at a completely inelastic boundary
It was shown in [2] that a Langevin process can be reflected at an energy absorbing boundary. Here, we establish that the law of this reflecting process can be characterized as the unique weak solution to a certain second order stochastic differential equation with constraints, which is in sharp contrast with a deterministic analog.
A silent-silent duel with randomly detected opponents
A simple remark on the conditioned square functions for martingale transforms
A stopping time problem on the positive integers
A time-dependent best choice problem with costs and random lifetime in organ transplants
This paper develops and analyzes a time-dependent optimal stopping problem and its application to the decision making process concerning organ transplants. Offers (organs for transplant) appear at jump times of a Poisson process. The values of the offers are i.i.d. random variables with a known distribution function. These values express the degree of histocompatibility between the donor and the recipient. The sequence of offers is independent of the jump times of the Poisson process. The decision...