The multilevel Monte Carlo and the control-variate method are reviewed for simulation of Coulomb collisions. The test case considered is fast-ion relaxation from ion-ion and electron-ion collisions against a Maxwellian background. A simplified energy scattering model is derived and related to the Cox-Ingersoll-Ross model for which, an exact time dependent solution can be obtained. The exact mod...

Global optimization is widely used in various aspects both in industry and academia. Although different methods in operations research have been proposed to solve the global optimization, simulated annealing and its variations have been favored for their simplicity in the implementation. In order to reach the global optimum from the current solution, a walking mechanism must be planned so that ...

In this paper we present a simple control variate method, for options pricing under stochastic volatility models by the risk-neutral pricing formula, which is based on the order moment of the stochastic factor Yt of the stochastic volatility for choosing a non-random factor Y (t) with the same order moment. We construct the control variate using a stochastic differential equation with a determi...

Other than common random numbers, control varlates is the most promising variance reduction technique in terms of its potential for widespread use: Control variates is applicable in single or multiple response simulation, it does not require altering the simulation run in any way, and any stochastic simulation contains potential control variates. A rich theory of control variates has been devel...

Noninvasive breath tests for gastric emptying are important techniques for understanding the changes in gastric motility that occur in disease or in response to drugs. Mice are often used as an animal model; however, the gamma variate model currently used for data analysis does not always fit the data appropriately. The aim of this study was to determine appropriate mathematical models to bette...

We discuss recent results on the complexity and tractability of problems dealing with ∞-variate functions. Such problems, especially path integrals, arise in many areas including mathematical finance, quantum physics and chemistry, and stochastic differential equations. It is possible to replace the ∞-variate problem by one that has only d variables since the difference between the two problems...