An important consequence of the fundamental theorem of integral and differential calculus is the fact every differentiation rule has an integration counterpart. Consider, for example, the chain rule (f ◦ g)′(t) = f′(g(t)) · g′(t). Then

which is just the substitution or change-of variable rule for integrals. Moreover, it provides a useful calculus formula if we want to evaluate integrals.

Let (B_{t})_{t≥0} be a BM^{1} and ()_{t≥0} an admissible, right-continuous complete filtration, e. g. , cf. Theorem 6.21. Itô’s formula is the stochastic ...

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