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Scientists have long been interested in problems of extremal laws. The relation betweenextremality and martingale representation property was discovered by Dellacherie, and was taken further andgiven its definite form by Jacod and Yor. Concept of statistical causality is closely connected to theextremality of measure. Namely, for weakly unique solutions of stochastic differential equations driven with semimartingales,can be established equivalence between the concept of causality and extremal measures of the solutions. The same can be proved for the solution of the martingale problem, too.

filtration, causality, extremal measures, stochastic differential equations