General Conditions of Weak Convergence of Discrete-Time Multiplicative Scheme to Asset Price with Memory

We present general conditions for the weak convergence of a discrete-time additive scheme to a stochastic process with memory in the space D [ 0 , T ] . Then we investigate the convergence of the related multiplicative scheme to a process that can be interpreted as an asset price with memory. As an example, we study an additive scheme that converges to fractional Brownian motion, which is based on the Cholesky decomposition of its covariance matrix. The second example is a scheme converging to the Riemann–Liouville fractional Brownian motion. The multiplicative counterparts for these two schemes are also considered. As an auxiliary result of independent interest, we obtain sufficient conditions for monotonicity along diagonals in the Cholesky decomposition of the covariance matrix of a stationary Gaussian process.

Thermodynamic properties of silicon containing acetylene peroxides

A technique for the explosion combustion of liquid organosilicon peroxides has been developed. Five Silicon containing acetylene peroxides have been investigated thermodynamically. Their combustion and evaporation enthalpies have been determined. Formation enthalpies of the compounds concerned in the condensed and gaseous states have been calculated. The magnitudes of two fragments for Benson additive scheme of formation enthalpies have been determined.