The method of moments is a simple, efficient method simulating polymerization processes. Its use is said to be limited in nonlinear free radical polymerizations with branching or crosslinking due to the assumptions needed. Here, moment equations are derived without assuming steady state, one radical per molecule, or a statistical distribution of connections. Equations are valid up to the gel point. The bulk solution is formally identical to the pseudo kinetic approach by Tobita and Hamielec if moments of dead polymer are replaced by the sum of dead and life polymers. The method relies on analytical solutions of the moments of the molecular weight distributions (MWD) of instantaneous primary chains. In emulsion polymerization compartmentalization of radicals complicates the calculation. An alternative approximation of these MWDs is presented. The present extension allows nonlinear free radical polymerization to be readily included in the computer based design and optimization of polymerization processes and to check more detailed calculations of the MWD.
In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes{B_n(s,t)},n∈N defined by B_n(s,t)=∫_0~s ∫_0~tk_(a(s))(s,u)K_(β(t))(t,u)θ_(n(u,v))dudv,here {θ_n(u, v)}n∈N is a family of processes, converging in law to a Brownian sheet as n→∞,based on the well known Donsker's theorem. 相似文献
In this paper,we consider a Markov switching Lévy process model in which the underlying risky assets are driven by the stochastic exponential of Markov switching Lévy process and then apply the model to option pricing and hedging.In this model,the market interest rate,the volatility of the underlying risky assets and the N-state compensator,depend on unobservable states of the economy which are modeled by a continuous-time Hidden Markov process.We use the MEMM(minimal entropy martingale measure) as the equivalent martingale measure.The option price using this model is obtained by the Fourier transform method.We obtain a closed-form solution for the hedge ratio by applying the local risk minimizing hedging. 相似文献