Ramblings on Malliavin Calculus
This entire web book was created so I can explain the topics of Malliavin Calculus and the Clark-Ocone formula to myself. After many months of frustration, I figured the main obstacle with learning the topic is the emphasis on mathematical rigor over pedagogical clarity, so I hope to bridge that gap. I’m assuming just basic knowledge of algebra, analysis and probability. I start with developing what Malliavin calculus was meant to address. I approach it in an indirect, meandering way. After documenting situations were a problem exists, the need for a solution will generate a “vacuum” of sorts. Following that, again indirectly, I lay the foundation step by step. Finally, the vacuum is filled. As mentioned, pedagogical clarity is the guiding factor. I’ll disregard proofs if I don’t see them important. Shortcuts will be taken liberally. Some pieces will lead nowhere or be there just to round up a concept. I may even admit when I’m ignorant about something and leave it like that. Truth is, I’m not a mathematician, a statistician or an economist. I’m just trying to understand an obscure topic.
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Comments
The introduction would benefit from more background on notation and terminology, or at least an indication of required background. The prosaic style is fantastic, and the fish example is great for keeping the topic grounded. Maybe consider drawing back to the trout more frequently to help explain new concepts.
4.3Content seems fine. The accessibility bar is a bit high, especially for those not frequently engaging in the equation symbols. It might be nice to have a bit more lead-up for the casual reader. Possibly via an offsite link?
4.4A very nice discussion.
7.2This is indeed rambling. It doesn’t even have a motivation at the start, or much explanation of what is going on. It’s also preposterously long.
2.9