For a continuous "d"-dimensional semimartingale "X" = ("X"1...,"X""d") and twice continuously differentiable function "f" from R"d" to R, it states that "f"("X") is a semimartingale and,:formula_18This differs from the chain rule used in standard calculus due to the term involving the quadratic covariation ["X""i","X""j" ].
A consequence of this is that the quadratic variation process of a stochastic integral is equal to an integral of a quadratic variation process,:: formula_21:formula_24== Лемма Ито ==: formula_251,…,"X""d") and twice continuously differentiable function "f" from R"d" to R, it states that "f"("X") is a semimartingale and,: formula_25This differs from the chain rule used in standard calculus due to the term involving the quadratic covariation ["X""i","X""j" ].