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Stochastic Integrals A random variable S is called the Itˆo integral of a stochastic process g(t,ω) with respect to the Brownian motion W(t,ω) on the interval 0,T if lim N→∞ E (S − ∑N i=1 g(ti−1,ω) W(ti,ω) − (W(ti−1,ω) = 0, (11) for each sequence of partitions (t0,t1,,tN) of the interval 0,T such thatmaxi(ti − ti−1) → 0 The limit in the above definition.
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