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  1. Jul 2025
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    1. bobbiethebobman 10 Jul 2025
      Proposition 3. (Itˆo’s lemma) For a given Itˆo processdSt = a(t, St)dt + b(t, St)dWt,the “stochastic” differential of a real-valued function X(t, St) (which is at least one timedifferentiable in t and twice in St) isdXt =( ∂Xt∂t + ∂Xt∂Sta(t, St) + 12∂2Xt∂S2tb(t, St)2)dt + ∂Xt∂Stb(t, St)dW

      Not a mistake, I'm just struggling to understand because it feels like by turning (dWt)^2 into dt, (I know it's because of var) it feels like we are "losing randomness", I must be missing some fundamental understanding

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  3. Jun 2025
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    5. bobbiethebobman 14 Jun 2025
      for each s ⊆ R

      Just a question: If we had given intervals of s, like we said s = [1,3], then I totally understand what F-measurable means, it's like high = between 1 and 3, if o-algebra includes the set of all high sample points then it's F measurable - so for a given "division" s, we can look and see if it's F-measureable - But this gives us no specific s and just tells us it's F-measureable. idk

      JAQ
    6. bobbiethebobman 14 Jun 2025
      even E0, E2, ..., En, P (∪ni=0Ei) = ∑ni=0 P(Ei).

      small typo "even", but also I'm confused, first we used F to refer to events, now it's E? : (. very unsettling for a sensitive young man like myself

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    3. bobbiethebobman 13 Jun 2025
      for each s ⊆ R

      If we had given intervals of s, like we said s = [1,3], then I totally understand what F-measurable means, it's like high = between 1 and 3, if o-algebra includes the set of all high sample points then it's F measurable, but s never feels embedded in S? Idk, this is frustrating.

      just a question
    5. bobbiethebobman 13 Jun 2025
      even E0, E2, ..., En, P (∪ni=0Ei) = ∑ni=0 P(Ei)

      small typo "even", but also I'm confused, first we used F to refer to events, now it's E? : (. very unsettling for a sensitive young man like myself

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