# Simulation methods and error analysis for trawl processes and ambit fields

arXiv: https://arxiv.org/abs/2208.08784 · HTML: https://mlsanity.com/paper/2208.08784/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Aug 2022.

## Built on by (most cited first, 2 of 2)

- [Likelihood-based inference and forecasting for trawl processes: a stochastic optimization approach](https://mlsanity.com/paper/2308.16092/) (2023)
- [Orlicz regrets to consistently bound statistics of random variables with an application to environmental indicators](https://mlsanity.com/paper/2310.05168/) (2023)

## Abstract (arXiv)

Trawl processes are continuous-time, stationary and infinitely divisible processes which can describe a wide range of possible serial correlation patterns in data. In this paper, we introduce new simulation algorithms for trawl processes with monotonic trawl functions and establish their error bounds and convergence properties. We extensively analyse the computational complexity and practical implementation of these algorithms and discuss which one to use depending on the type of L'evy basis. We extend the above methodology to the simulation of kernel-weighted, volatility modulated trawl processes and develop a new simulation algorithm for ambit fields. Finally, we discuss how simulation schemes previously described in the literature can be combined with our methods for decreased computational cost.