# On the Measurability of Stochastic Fourier Integral Operators

## TL;DR

This paper investigates the measurability of stochastic Fourier integral operators, demonstrating their continuous dependence on random phase and amplitude functions, with applications to wave equations in random media.

## Contribution

It proves the continuity of FIOs with respect to their random phase and amplitude functions, enabling analysis of stochastic wave phenomena.

## Key findings

- FIOs depend continuously on their phase and amplitude functions
- Results apply to solutions of transport equations with random speeds
- Applicable to wave propagation in random media

## Abstract

This work deals with the measurability of Fourier integral operators (FIOs) with random phase and amplitude functions. The key ingredient is the proof that FIOs depend continuously on their phase and amplitude functions, taken from suitable classes. The results will be applied to the solution FIO of the transport equation with spatially random transport speed as well as to FIOs describing waves in random media.