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

Matija Vidmar

Statistics & Probability Letters, 2021, vol. 175, issue C

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.

Keywords: Stochastic equations; Equiprobable random signs; Non-anticipative weak solutions; Nonmeasurable sets; Kolmogorov’s zero–one law (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2021.109117

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