scholarly journals Some new results on relative entropy production, time reversal, and optimal control of time-inhomogeneous diffusion processes

2021 ◽  
Vol 62 (4) ◽  
pp. 043302
Author(s):  
Wei Zhang
Keyword(s):  
Optimal Control ◽  
Entropy Production ◽  
Relative Entropy ◽  
Time Reversal ◽  
Diffusion Processes ◽  
Production Time ◽  
Inhomogeneous Diffusion

Complete monotonicity of entropy production in chemical reaction

1981 ◽  
Vol 46 (2) ◽  
pp. 452-456
Author(s):  
Milan Šolc
Keyword(s):  
Entropy Production ◽  
Equilibrium Constant ◽  
Chemical Reaction ◽  
Relative Entropy ◽  
Order Reaction ◽  
Complete Monotonicity ◽  
First Order Reaction ◽  
First Order ◽  
Completely Monotonic ◽  
Derivatives Of

The successive time derivatives of relative entropy and entropy production for a system with a reversible first-order reaction alternate in sign. It is proved that the relative entropy for reactions with an equilibrium constant smaller than or equal to one is completely monotonic in the whole definition interval, and for reactions with an equilibrium constant larger than one this function is completely monotonic at the beginning of the reaction and near to equilibrium.

Sequential Monte Carlo methods for diffusion processes

2009 ◽  
Vol 465 (2112) ◽  
pp. 3709-3727 ◽  
Author(s):  
Ajay Jasra ◽  
Arnaud Doucet
Keyword(s):  
Optimal Control ◽  
Monte Carlo ◽  
Option Pricing ◽  
Monte Carlo Methods ◽  
Sequential Monte Carlo ◽  
Diffusion Processes ◽  
Time Discretization ◽  
Initial Condition ◽  
Sequential Monte Carlo Methods ◽  
Low Dimensional

In this paper, we show how to use sequential Monte Carlo methods to compute expectations of functionals of diffusions at a given time and the gradients of these quantities w.r.t. the initial condition of the process. In some cases, via the exact simulation of the diffusion, there is no time discretization error, otherwise the methods use Euler discretization. We illustrate our approach on both high- and low-dimensional problems from optimal control and establish that our approach substantially outperforms standard Monte Carlo methods typically adopted in the literature. The methods developed here are appropriate for solving a certain class of partial differential equations as well as for option pricing and hedging.

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