Differentiability Conditions for Applying Ito’s Lemma

Summary

The document asks what regularity a function needs for Ito’s lemma to describe a function of a geometric Brownian process. Its brief answer adds that the function must be twice differentiable, beyond being continuous.

The exchange offers no derivation, examples, or discussion of the precise technical conditions, such as continuity requirements on the derivatives or variants of Ito’s formula. Treat the answer as a basic rule of thumb rather than a complete statement of the theorem’s assumptions.

Key ideas

• Ito’s lemma is used to derive the stochastic process followed by a function of a geometric Brownian process.
• The answer says continuity alone is insufficient and the function must also be twice differentiable.
• The document does not specify the full regularity conditions or demonstrate their application.

Tags

# Applicability of the Ito's lemma


# Applicability of the Ito's lemma












`Ito's lemma` is used to find the `stochastic process` of the function of a `Geometric Brownian process`.

My question, is there any limitation of the kind of function that can be considered for correctly using the `Ito's lemma`, apart from just being continuous everywhere within the domain of the function?

Any insight will be highly helpful

## Answer by Bob Jansen (score 0)

https://quant.stackexchange.com/a/55836

It also needs to be twice differentiable.

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