Crystallization process, Johnson–Mehl tessellations, Nelson–Aalen estimator, Kaplan–Meier estimator, Primary 62N02, Secondary 62P30, Secondary 60G55,

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Set-indexed stochastic analysis and set-indexed stochastic calculus are faced here with a new approach of dimension's reduction. We introduce a new tool (main flow) in order to deal with one-parameter calculus in set-indexed framework. We prove an Itô formula for any Brownian functional where the Brownian component is not a martingale on the whole set of indices but induces such a martingale. As first extensions, we provide definitions of bracket and local time in set-indexed context.

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