Stochastic Stability of Processes Determined by Poisson Differential Equations with Delay

We prove an existence theorem and establish the property of stochastic stability for processes determined by the Poisson stochastic differential equations with delay.     

A central limit theorem for nonhomogeneous semi-Markov random evolutions

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 8, pp. 1064–1070, August, 1989.     

Filtration of components of processes of random evolution

The problem of estimation of a nonobservable component θ_t for a two-dimensional process (θ_t, ξ_t) of random evolution (θ _t,ξ_t);x_t, 0≤t≤T, is investigated on the basis of observations of ξ_s. s≤t, where x _t is a homogeneous Markov process with infinitesimal operator Q. Applications to stochastic models of a (B,S)-market of securities is described under conditions of incomplete market. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 12, pp. 1701–1705, December, 1998.     

Weak convergence of semi-Markov random evolutions in an averaging scheme (martingale approach)

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 12, pp.1680–1686, December, 1989.     

Investigation of a linear evolution system in the Banach space with random times of perturbations

For a linear evolution system given in the Banach space and characterized by pulse perturbations at random times, we establish conditions for the existence of a unique solution of the Cauchy problem and investigate the stability of the zero solution. Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 3, pp. 433–436, March, 1998.     

Analog of the black-scholes formula for option pricing under conditions of (b, s, x)-incomplete market of securities with jumps

We describe a (B, S,X )-incomplete market of securities with jumps as a jump random evolution process that is a combination of an ltô process in random Markov medium and a geometric compound Poisson process. For this model, we derive the Black-Scholes equation and formula, which describe the pricing of the European call option under conditions of (B,S,X)-mcomplete market.     

2-Amino-3-(benzimidazol-2-yl)benzo[b]furans

The corresponding 2-amino-3-(benzimidazol-2-yl)benzo[b]furans were obtained by reaction of 2,3,5-trimethyl-1,4-benzoquinone with 2-cyanomethylbenzimidazoles. It is shown that new benzo[b]furo[2′,3′∶4,5]pyrimido[1,6-a]benzimidazole polynuclear heterocyclic systems (bases and quaternary salts) are formed in the reaction of these products with acylating agents. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 164–166, February, 1980.     

Sterols of the fungusStachybotrys alternaus

Conclusions 1. The composition of the sterol fraction of the unsaponifiable group of substances of the fungusStachybotrys alternaus has been studied. It has been shown that, unlike the sterol fraction of other mycelial fungi, the sterol fraction studied contains almost no ergosterol.2. On the basis of UV, IR, mass, and NMR spectroscopy, optical activity, and chromatographic behavior, the substances present in the sterol fraction have been identified structurally, and the ratio of their quantities has been found.Khimiya Prirodnykh Soedinenii, Vol. 6, No. 3, pp. 319–322, 1970