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Then its Ito integral from a to b is b a X tdW. W ti 186 wh er e the ti ar e as in Denition 186 trunc ate d below by a and ab ove by b. Derivation Of Ito S Lemma Youtube The resulting integral will agree with the Ito integral when both are defined. Ito integral of wiener process . We consider two Ito integrals. As Nate Eldredge already pointed out the Wiener process is a stochastic process and so the integral of a function of a Wiener process is a random variable. 5142016 It is known fact that definite integral of standard Wiener process from 0 to t results in another Gaussian process with slice distribution that is normal distributed with mean equal to 0 and variance T3 3 i-e t 0Wsds N0 t3 3 Question. 12 Hu Yaozhong Lu Fei and Nualart David Annals of Probability 2012. Meanwhile Ito-Liu integral is the counterpart of Ito integral in stochastic process and Liu integral in fuzzy process. 1162dxt ω ft ωdt gt ωdW tω Here f t ω t ab is a second-order mean-square continuous proc