arXiv subjects

Assil Fadle

Publications and source records attributed to Assil Fadle.

2 recordsLinked to original sources

arXiv2024

It\=o and It\=o-Wentzell chain rule for flows of conditional laws of continuous semimartingales: an easy approach

We provide a general It\=o\,-Wentzell formula for a random field of maps on the Wasserstein space of probability measures, defined by continuous semimartingales, and evaluated along the flow of conditional distributions of another continuous semimartingale. Our method follows standard arguments of It\=o calculus, and thus bypasses the approximation by empirical measures commonly used in the existing literature. As an application, we derive the dynamic programming equation for a mean field stochastic control problem with common noise.

math.PR↗

arXiv2020

Unsteady Wave Drag on a Disturbance Moving Along an Arbitrary Trajectory

We derive analytical formulas for the wake and wave drag of a disturbance moving arbitrarily at the air-water interface. We show that, provided a constant velocity is reached in finite time, the unsteady surface displacement converges to its well-known steady counterpart as given by Havelock's famous formula. Finally we assess, in a specific situation, to which extent one can rightfully use Havelock's steady wave drag formula for non-uniform motion (quasi-static). Such an approach can be used to legitimize or discredit a number of studies which used steady wave drag formulas in unsteady situations.

physics.flu-dyn↗