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A nonclassical solution to a classical SDE and a converse to Kolmogorov’s zero–one law

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  • Vidmar, Matija

Abstract

For a discrete-negative-time discrete-space SDE, which admits no strong solution in the classical sense, a weak solution is constructed that is a (necessarily nonmeasurable) non-anticipative function of the driving i.i.d. noise. The result highlights the strong rôle measurability plays in (non-discrete) probability. En route one — quite literally — stumbles upon a converse to the celebrated Kolmogorov’s zero–one law for sequences with independent values.

Suggested Citation

  • Vidmar, Matija, 2021. "A nonclassical solution to a classical SDE and a converse to Kolmogorov’s zero–one law," Statistics & Probability Letters, Elsevier, vol. 175(C).
    • Handle: RePEc:eee:stapro:v:175:y:2021:i:c:s0167715221000791
    DOI: 10.1016/j.spl.2021.109117
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    References listed on IDEAS

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    1. Vladimir Vovk, 2017. "The role of measurability in game-theoretic probability," Finance and Stochastics, Springer, vol. 21(3), pages 719-739, July.
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