A nonclassical solution to a classical SDE and a converse to Kolmogorov's zero–one law
| Autor: | Matija Vidmar |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Statistics and Probability
nonmeasurable sets Pure mathematics Weak solution 010102 general mathematics stohastične enačbe Function (mathematics) neanticipirajoča šibka rešitev Kolmogorov's zero–one law 01 natural sciences 010104 statistics & probability nemerljive množice non-anticipative weak solutions Converse stochastic equations equiprobable random signs 0101 mathematics Statistics Probability and Uncertainty udc:519.216 enako verjetni slučajni predznaki Zero–one law Mathematics Kolmogorov zakon nič – ena |
| Zdroj: | Statistics & probability letters, vol. 175, 109117, 2021. |
| ISSN: | 0167-7152 |
| Popis: | 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 role 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. |
| Databáze: | OpenAIRE |
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