Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation.

Gyration Radius and Energy Study at Different Temperatures for Acetylcholine Receptor Protein in Gas Phase by Monte Carlo, Molecular and Langevin Dynamics Simulations

The determination of gyration radius is a strong research for configuration of a Macromolecule. Italso reflects molecular compactness shape. In this work, to characterize the behavior of theprotein, we observe quantities such as the radius of gyration and the average energy. We studiedthe changes of these factors as a function of temperature for Acetylcholine receptor protein in gasphase with n...

Energy study at different solvents for potassium Channel Protein by Monte Carlo, Molecular and Langevin Dynamics Simulations

Potassium Channels allow potassium flux and are essential for the generation of electric current acrossexcitable membranes. Potassium Channels are also the targets of various intracellular controlmechanisms; such that the suboptimal regulation of channel function might be related to pathologicalconditions. Realistic studies of ion current in biologic channels present a major challenge for compu...

The multilevel Monte-Carlo Method for stochastic differential equations driven by jump-diffusion processes

In this article we discuss the multilevel Monte Carlo method for stochastic differential equations driven by jump-diffusion processes. We show that for a reasonable jump intensity the multilevel Monte Carlo method for jump-diffusions reduces the computational complexity compared to the standard Monte Carlo method significantly for a given mean square accuracy. Carrying out numerical experiments...

Fractional Langevin Monte Carlo: Exploring Lévy Driven Stochastic Differential Equations for MCMCSUPPLEMENTARY DOCUMENT

Stabilized multilevel Monte Carlo method for stiff stochastic differential equations

A multilevel Monte Carlo (MLMC) method for mean square stable stochastic differential equations with multiple scales is proposed. For such problems, that we call stiff, the performance of MLMC methods based on classical explicit methods deteriorates because of the time step restriction to resolve the fastest scales that prevents to exploit all the levels of the MLMC approach. We show that by sw...