On the exchange of intersection and supremum of sigma-fields in filtering theory

We construct a stationary Markov process with trivial tail sigma-field and a nondegenerate observation process such that the corresponding nonlinear filtering process is not uniquely ergodic. This settles in the negative a conjecture of the author in the ergodic theory of nonlinear filters arising from an erroneous proof in the classic paper of H. Kunita (1971), wherein an exchange of intersection and supremum of sigma-fields is taken for granted.Comment: 20 page

Asymptotic equivalence of discretely observed diffusion processes and their Euler scheme: small variance case

This paper establishes the global asymptotic equivalence, in the sense of the Le Cam $\Delta$-distance, between scalar diffusion models with unknown drift function and small variance on the one side, and nonparametric autoregressive models on the other side. The time horizon $T$ is kept fixed and both the cases of discrete and continuous observation of the path are treated. We allow non constant diffusion coefficient, bounded but possibly tending to zero. The asymptotic equivalences are established by constructing explicit equivalence mappings.Comment: 21 page

Economic Interests and the Economic Mechanism

The Twenty-fifth Party Congress pointed to the need for the more skillful use of economic incentives and levers: cost accounting, profits, prices, and bonuses. "In other words," the Report of the Central Committee of the Communist Party of the Soviet Union (CPSU) stated, "the entire system of indicators that are used to evaluate the performance of ministries, associations, and enterprises, especially the effectiveness and quality of their work, requires improvement. These indicators are designed to unify the interests of personnel with the interests of the enterprise, and the interests of the enterprise with the interests of the state. They are intended to inspire the adoption (and fulfillment) of intensive plans, the saving of resources, the lowering of the enterprise cost of production. At the same time, they should result in the more rapid development of new products and the production of high-quality products in the required assortment."

The Path to Privatization

A little less than half of all deliveries are now the subject of direct barter relations between enterprises. Naturally the barter system cannot secure the normal functioning of a modern economy. And since it is impossible to restore the administrative system, the situation will deteriorate until one or another program for the liberalization of prices and economic relationsâa program of making the transition to a marketâis implemented. It is only a question of what it will be like.