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Stochastic Calculus on Filtered Probability Spaces

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Book cover Probability Theory III

Part of the book series: Encyclopaedia of Mathematical Sciences ((EMS,volume 45))

Abstract

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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Authors
  1. R. Sh. Liptser
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  2. A. N. Shiryaev
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Liptser, R.S., Shiryaev, A.N. (1998). Stochastic Calculus on Filtered Probability Spaces. In: Probability Theory III. Encyclopaedia of Mathematical Sciences, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03640-2_3

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  • DOI: https://doi.org/10.1007/978-3-662-03640-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08122-4

  • Online ISBN: 978-3-662-03640-2

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