Fast reaction limit and forward-backward diffusion: A Radon–Nikodym approach

Backward and Forward equations for Diffusion processes

This section is devoted to the discussion of two fundamental (partial) differential equations, that arise in the context of Markov diffusion processes. After giving a brief introduction of continuous-time continuous state Markov processes, we introduce the forward and backward equation, and provide a heuristic derivation of these equations for diffusion processes. We also discuss some examples ...

Backward and forward path following control of a wheeled robot

A wheeled mobile robot is one of the most important types of mobile robots. A subcategory of these robots is wheeled robots towing trailer(s). Motion control problem, especially in backward motion is one of the challenging research topics in this field. In this article, a control algorithm for path-following problem of a tractor-trailer system is provided, which at the same time provides the ab...

Forward and Backward Uncertainty Quantification in Optimization

This contribution gathers some of the ingredients presented during the Iranian Operational Research community gathering in Babolsar in 2019.It is a collection of several previous publications on how to set up an uncertainty quantification (UQ) cascade with ingredients of growing computational complexity for both forward and reverse uncertainty propagation.

On the Central Limit Theorems for Forward and Backward Martingales

Let {Xi}i≥1 be a martingale difference sequence with Xi = Si − Si−1. Under some regularity conditions, we show that (X 1+· · ·+X2 Nn)SNn is asymptotically normal, where {Ni}i≥1 is a sequence of positive integer-valued random variables tending to infinity. In a similar manner, a backward (or reverse) martingale central limit theorem with random indices is provided. Keywords—central limit theorem...

Global existence and fast-reaction limit in reaction-diffusion systems with cross effects