Convergence Orders for Mixed SDE Discretization Schemes

Summary

The document asks whether two correlated stochastic differential equations can use different numerical discretization schemes. In particular, it compares using Euler discretization for both processes with using Euler for one and Milstein for the other, and asks whether references address such mixed schemes.

It provides no proposed method, analysis, references, or experimental evidence. Its central issue is how combining schemes of different accuracy affects convergence order when the underlying SDEs are correlated. Any answer would depend on the equations, the way their correlated noise is implemented, and the convergence criterion; these details are not supplied, so the document leaves the question open.

Key ideas

• The question concerns discretizing two correlated stochastic differential equations with different schemes.
• It contrasts using Euler for both equations with mixing Euler and Milstein.
• The main concern is the convergence order of a mixed-scheme approximation.
• The document supplies no equations, references, analysis, or empirical evidence.

Tags

# Discretization Schemes


# Discretization Schemes












I am working with two correlated SDE's and I was wondering if I could use two different discretization schemes for them. Is there maybe a reference of this being done? And can something be said about the convergence order? Is it better to use two Euler discretizations in stead of 1 Euler and 1 Milstein?

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