Vladimir Rotar

Limit theorems for polylinear forms

The limit theorems for polylinear forms are obtained. Conditions are found under which the distribution of the polylinear form of many random variables is essentially the same as if all the distributions of arguments were normal.

A remark on quadrant normal probabilities in high dimensions

This paper provides an asymptotic evaluation of the quadrant probability P(Y1[less-than-or-equals, slant]b,...,Yt[less-than-or-equals, slant]b) as t-->[infinity], where the Yis are exchangeable normals with a correlation [rho]. This probability is often represented as , where [Phi] is the standard normal distribution, and a=(1-[rho])/[rho].

Optimality in probability and almost surely. the general scheme and a linear regulator problem

This paper studies one dimensional diffusion with controlled drift. We give definitions of an almost surely optimal policy and a policy optimal in probability. These types of optimality are much stronger than the classical optimality for the expected limiting average per unit time cost (optimality in mean on [0,∞)). To analyse when an optimal in mean on [0,∞) policy is also optimal almost surely and in probability, we offer a simple direct method. This method is later applied for the stationary linear regulator with quadratic cost. The question of overtaking optimality is also discussed

On Optimality in Probability and Almost Surely for Processes with a Communication Property. I. The Discrete Time Case.

We establish conditions under which the strategy minimizing the expected value of a cost functional has a much stronger property; namely, it minimizes the random cost functional itself for all realizations of the controlled process belonging to a set, the probability of which is close to one for large time horizons. The main difference of the conditions mentioned from those obtained earlier is that the former do not deal with value function properties but concern a possibility of transition of the controlled process from one state to another in a time with a finite mean. It makes the verification of these conditions in a number of situations of the general form much easier. The first part of the paper concerns processes in discrete time; the second part will be devoted to processes in continuous time.

Some General Results on Equilibrium Prices in Large Random Exchange Economies

In this paper we are concerned with a model of a Walrasian exchange economy in which the preferences and endowments of the agents are random. Stochastic interaction among the agents is formally described in terms of dependency neighborhoods. The main result concerns a characterization of the distribution of market-clearing equilibrium prices in a large economy. The paper establishes conditions for asymptotic normality of appropriately normalized equilibrium prices.

Some Bounds on the Rate of Convergence in the CLT for Martingales. II

This paper concerns rates of convergence in the central limit theorem (CLT) for the random variables

On a Dyadic Parametrization of Curves

S_{n}=\sum_{1}^{n}X_{m}

Preferences and metric structures of spaces of alternatives

, where

On a Statistical Approach to Choice under Uncertainty

X_{m}

ON COUPLING CONSTRUCTIONS AND RATES IN THE CLT FOR DEPENDENT SUMMANDS WITH APPLICATIONS TO THE ANTIVOTER MODEL AND WEIGHTED U-STATISTICS

are martingale-differences. It is known that in the general case one cannot hope for a rate better than