Characterization of a regular family of semimartingales by line integrals

A characterization of a regular family of semimatingales as a maximal fasmily of processes with respect of which one can define a stochastic line integral with natural continuity properties is given.     

Corrections to the black body radiation due to minimum-length deformed quantum mechanics

Planck spectrum of black body radiation is usually derived by considering of quantized free electromagnetic field at a finite temperature. The minimum-length deformed quantization affects field theory both at the first and second quantization levels. Performing an exact calculation to the first order in deformation parameter, both of the corrections turn out to be of the same order. Nevertheless, the correction at the second quantization level has some qualitative difference, that may be interesting for future study to differentiate between these two sorts of corrections. In itself the correction to the black body radiation seems to be innocuous in light of the big-bang nucleosynthesis whenever the minimum length is less or equal to ¹⁰−19 cm.     

A Bayesian-martingale approach to the general disorder problem

We consider a Bayesian-martingale approach to the general change-point detection problem. In our setting the change-point represents a random time of bifurcation of two probability measures given on the space of right-continuous functions. We derive a reflecting backward stochastic differential equation (RBSDE) for the value process related to the disorder problem and show that in classical cases of the Wiener and Poisson disorder problems this RBSDE is equivalent to free-boundary problems for parabolic differential and differential–difference operators respectively.     

Diamond Synthesis in Cool Plasma

The conditions of low pressure autoepitaxy of diamond are analysed and theoretical concepts concerning the plasmochemical method of diamond synthesis put forward. The experimental method used is described. The obtained results have demonstrated the utility of the plasmochemical method for obtainment of diamond and confirmed the validity of the presented theoretical concepts.     

Weighted oscillator strengths and lifetimes for the Si II spectrum

The weighted oscillator strengths (gf) and the lifetimes for Si II presented in this work were carried out in a multiconfiguration Hartree–Fock relativistic (HFR) approach. In this calculation, the electrostatic parameters were optimized by a least-squares procedure, in order to improve the adjustment to experimental energy levels. This method produces gf-values that are in better agreement with intensity observations and lifetime values that are closer to the experimental ones. In this work we presented all the experimentally known electric dipole Si II spectral lines.     

New Proofs of Some Results on Bounded Mean Oscillation Martingales Using Backward Stochastic Differential Equations

Using properties of backward stochastic differential equations, we give new proofs of some well-known results on bounded mean oscillation (BMO) martingales and improve some estimates of BMO norms.     

The Electric Field Outside a Stationary Resistive Wire Carrying a Constant Current

We present the opinion of some authors who believe there is no force between a stationary charge and a stationary resistive wire carrying a constant current. We show that this force is different from zero and present its main components: the force due to the charges induced in the wire by the test charge and a force proportional to the current in the resistive wire. We also discuss briefly a component of the force proportional to the square of the current which should exist according to some models and another component due to the acceleration of the conduction electrons in a curved wire carrying a dc current (centripetal acceleration). Finally, we analyze experiments showing the existence of the electric field proportional to the current in resistive wires.     

Backward stochastic partial differential equations related to utility maximization and hedging

We study the utility maximization problem, the problem of minimization of the hedging error and the corresponding dual problems using dynamic programming approach. We consider an incomplete financial market model, where the dynamics of asset prices are described by an ℝ^d-valued continuous semimartingale. Under some regularity assumptions, we derive the backward stochastic PDEs for the value functions related to these problems, and for the primal problem, we show that the strategy is optimal if and only if the corresponding wealth process satisfies a certain forward SDE. As examples we consider the mean-variance hedging problem and the cases of power, exponential, logarithmic utilities, and corresponding dual problems. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 45, Martingale Theory and Its Application, 2007.