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

On the Principles of Price Formation

There is as yet no consensus in economic literature concerning the principles of price formation under socialism. The only point that can be considered as commonly recognized is the proposition that prices on products must reflect the socially necessary labor inputs (SNLI) associated with their production. While recognizing t h i s principle, some economists also emphasize that under socialism social utility must be the leading aspect of the unity of inputs and the utility manifested in the price. Other economists, to the contrary, reject the decisive role of social utility.

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 "Cultured Huckster" among Us: One the Restructuring of Economic Priorities

The time for >i>perestroika>/i> in our society is long overdue. This is the turth. At the same time, society turned out to be unprepared for an abrupt change of course. This relates not only to the restructuring of the economic and political system, but also to deep, oftentimes seemingly obviousor completely unconsciousideological and socio-psychological prerequisites, on which we base our actions and evaluations. One of these "obvious truths" is the view that the most important thing is to produce a product. To distribute a product (to sell it or dispense it) and to consume it is an easy matter.

Methods of Mathematical Economics and the Theory of Planning and Administering the Economy

The content of the theory of optimal planning and management of the economy is not simply that of applying mathematics and computers to plan calculations. One of the most pressing problems of this theory at the present time is that of designing a system of interrelationships among economic agencies and a system of stimuli that would immediately make possible the fullest employment of the tremendous opportunities for the use of economic techniques of management set forth by the September 1965 Plenum of the Central Committee of the CPSU and the 23rd Party Congress. The science of economics faces the task of creating a mechanism best capable of carrying out the functions of managing the economy to the greatest advantage. In a number of respects this requires a reinterpretation of the operation of economic mechanisms from the standpoint of the possibilities of employing them for optimal planning and management.