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On modelling physical systems with stochastic models: diffusion versus Lévy processes.

Cécile Penland¹, Brian D Ewald

¹NOAA/ESRL/Physical Sciences Division, 325 Broadway, Boulder, CO 80305, USA. cecile.penland@noaa.gov

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|May 8, 2008

Summary

This summary is machine-generated.

Numerical models for weather and climate increasingly use stochastic differential equations with random forcing. This review covers Gaussian white noise and Lévy processes, including numerical generation methods.

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Area of Science:

Atmospheric sciences
Climate modeling
Computational physics

Background:

Stochastic differential equations are crucial for modeling complex systems.
Multiscale interactions in weather and climate require advanced simulation techniques.
Random forcing components are essential for realistic numerical models.

Purpose of the Study:

To review fundamental properties of stochastic differential equations driven by Gaussian white noise.
To compare these systems with those described by stable Lévy processes.
To discuss numerical generation techniques for stochastic processes in climate models.

Main Methods:

Review of theoretical properties of stochastic differential equations.
Comparative analysis of Gaussian white noise and stable Lévy processes.
Exploration of numerical algorithms for stochastic process simulation.

Main Results:

Detailed examination of stochastic differential equations with Gaussian white noise.
Identification of key differences and similarities with stable Lévy processes.
Overview of practical methods for numerical implementation.

Conclusions:

Stochastic differential equations provide a robust framework for multiscale modeling.
Understanding different noise types (Gaussian vs. Lévy) is critical for model accuracy.
Efficient numerical generation is key to advancing climate simulations.