Large Deviations Principle for a Large Class of One-Dimensional Markov Processes

We study the large deviations principle for one dimensional, continuous, homogeneous, strong Markov processes that do not necessarily behave locally as a Wiener process. Any strong Markov process $X_{t}$ in $\mathbb{R}$ that is continuous with probability one, under some minimal regularity conditions, is governed by a generalized elliptic operator $D_{v}D_{u}$, where $v$ and $u$ are two strictly increasing functions, $v$ is right continuous and $u$ is continuous. In this paper, we study large deviations principle for Markov processes whose infinitesimal generator is $\epsilon D_{v}D_{u}$ where $0<\epsilon\ll 1$. This result generalizes the classical large deviations results for a large class of one dimensional "classical" stochastic processes. Moreover, we consider reaction-diffusion equations governed by a generalized operator $D_{v}D_{u}$. We apply our results to the problem of wave front propagation for these type of reaction-diffusion equations.Comment: 23 page

Meson Structure in Deep Inelastic Scattering

We study the deep inelastic structure functions of mesons within the Nambu and Jona-Lasinio model. We calculate the valence quark distributions in $\pi$, $K$, and $\rho$ mesons at the low energy model scale, which are evoluted to the experimental momentum scale in terms of the Altarelli-Parisi equation. The resulting distribution functions show reasonable agreements with experiment. We also discuss the semi-inclusive lepton nucleon scattering process with a slow nucleon in coincidence in the final state, which reveals the off-shell structure of the pion.Comment: 31 pages with 16 figures as uuencoded postscript files, TMU-NT-940101 (plain LaTeX

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.