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...The annals of applied probability vol no stochasticcalculusforbrownian motiononabrownianfracture by davarkhoshnevisan andthomasm lewis university utah and furman in this paper we give a pathwise development stochastic integrals with respect to iterated brownian motion also provide detailed analysis variations these are linked random scenery itself introduction preliminaries heat ow on fractal has been subject recent vigorous investigations see for example survey article as classical studies smooth manifolds probabilistic interpretation such problems comes from descrip tion canonical process which is usually called one many areas applications along fractures vein articles start an idealized fracture simple geometric construct comb proceed construction let us attack problem different point view namely rather than considering xed begin idealization be vertically homogeneous two dimensional rectangular medium sides parallel axes then left right would resemble graph dimen sional make more p...