Summer of Math Exposition

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.