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Stochastic Calculus On Filtered Probability Spaces

R. Liptser, A. Shiryaev
Published 1998 · Mathematics

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Kolmogorov’s axioms of probability theory give an approach, generally accepted at the present time, to the mathematical description of probabilistic-statistical phenomena. The problem of axiomatizing probability theory was formulated in the Sixth problem of D. Hilbert in his famous address of 8 August 1900 at the Second International Congress of Mathematicians in Paris. Hilbert, who included probability theory in physics (as was the general acceptance at the time), formulated the 6th problem as “The mathematical statement of the axioms of physics” (Hilbert 1901): “Closely connected with investigations into the foundations of geometry is the problem of axiomatizing the construction within that same framework of those physical disciplines in which mathematics already plays a distinguished role: in the first place, this is the theory of probability and mechanics.
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