34F05 Ordinary differential equations and systems with randomness

Overview

34F05 studies ordinary differential equations and systems with randomness in equations with randomness. It studies differential equations with random forcing, coefficients, or initial data, combining ODE ideas with probability.

Related Wikipedia Page

Equations With Randomness (Wikipedia)

Useful Links

• Equations With Randomness (Wikipedia)
• Stochastic differential equation (Wikipedia)
• Stochastic process (Wikipedia)

Key Ideas

• Canonical formulations and representative examples for ordinary differential equations and systems with randomness
• How structural, local, and computational viewpoints interact in the subject
• Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in stochastic modeling, finance, and random dynamical systems.

Applications

• Stochastic dynamics
• Numerical SDE methods
• Randomly perturbed systems

References

• Øksendal, B. (2003) Stochastic Differential Equations. 6th edn. Springer.
• Kloeden, P.E. and Platen, E. (1992) Numerical Solution of Stochastic Differential Equations. Springer.

Recommended Textbooks

• Mao, X. (2007) Stochastic Differential Equations and Applications. 2nd edn. Horwood.
• Arnold, L. (1974) Stochastic Differential Equations: Theory and Applications. Wiley.