Memory-controlled diffusion

Controlled diffusion processes ∗ , †

This article gives an overview of the developments in controlled diffusion processes, emphasizing key results regarding existence of optimal controls and their characterization via dynamic programming for a variety of cost criteria and structural assumptions. Stochastic maximum principle and control under partial observations (equivalently, control of nonlinear filters) are also discussed. Seve...

Controlled Jump Diffusion

This paper concerns the optimal stopping time problem in a nite horizon of a controlled jump diiusion process. We prove that the value function is continuous and is a viscosity solution of the inte-grodiierential variational inequality arising from the associated dynamic programming. We also establish comparison principles, which yield uniqueness results. Moreover, the viscosity solution approa...

Diffusion-Controlled Reaction Kinetics

Diffusion-Controlled Hysteresis

A new model of time-dependent sorption-desorption hysteresis is presented. This type of hysteresis is not related to transitions between metastable adsorption states, which are a common cause of capillary condensation hysteresis in mesoporous materials. We show that time-dependent hysteresis is a consequence of slow kinetics and failure to reach equilibrium at given experimental conditions. The...

Gated Diffusion-controlled Reactions

The binding and active sites of proteins are often dynamically occluded by motion of the nearby polypeptide. A variety of theoretical and computational methods have been developed to predict rates of ligand binding and reactivity in such cases. Two general approaches exist, "protein centric" approaches that explicitly treat only the protein target, and more detailed dynamical simulation approac...