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Stochastic Calculus

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2 domain-specific abstractions whose origin domain is Stochastic Calculus.

  • Doléans–Dade Exponential — Map a semimartingale driver to the unique multiplicative process solving dZ = Z_- dX, with continuous quadratic-variation and jump-product corrections that ordinary exponentiation omits.
  • Itô isometry — The equality identifying the second moment of an Itô integral with the expected time integral of the squared adapted integrand.