On a functional equation of Luce.
On two combination rules for 0-1-sequences.
Optimal decision rules
Optimal token allocation in solitaire knock'm down.
Parrondo's paradox.
Reflected forward-backward SDEs and obstacle problems with boundary conditions.
Saturations of gambling houses
Stochastic control optimal in the Kullback sense
The paper solves the problem of minimization of the Kullback divergence between a partially known and a completely known probability distribution. It considers two probability distributions of a random vector on a sample space of dimensions. One of the distributions is known, the other is known only partially. Namely, only the conditional probability distributions of given are known for . Our objective is to determine the remaining conditional probability distributions of given such...
Stochastic Duels with Correlated Fire.
The game as a contract and the “risicum" in the work of Olivi. (Le jeu comme contrat et le risicum chez Olivi.)
Two game-set inequalities.
Two-player knock 'em down.
Weak infinitesimal operators and stochastic differential games.
This article considers the problem of finding the optimal strategies in stochastic differential games with two players, using the weak infinitesimal operator of process xi the solution of d(xi) = f(xi,t,u1,u2)dt + sigma(xi,t,u1,u2)dW. For two-person zero-sum stochastic games we formulate the minimax solution; analogously, we perform the solution for coordination and non-cooperative stochastic differential games.
Weighted entropies
We present an axiomatic characterization of entropies with properties of branching, continuity, and weighted additivity. We deliberately do not assume that the entropies are symmetric. The resulting entropies are generalizations of the entropies of degree α, including the Shannon entropy as the case α = 1. Such “weighted” entropies have potential applications to the “utility of gambling” problem.
-equilibria in many-player stochastic differential games
In this paper -person nonzero-sum games are considered. The dynamics is described by Ito stochastic differential equations. The cost-functions are conditional expectations of functionals of Bolza type with respect to the initial situation. The notion of -equilibrium is introduced in many-player stochastic differential games. Some properties of -equilibria are analyzed. Sufficient conditions are established guaranteeing the -equilibrium for the strategies of the players. In a particular case...
Оценка распределения момента остановки для одной стохастической системы