Discrete hilbert transform à la gundy-Varopoulos
| Autor: | Nicola Arcozzi, Stefanie Petermichl, Komla Domelevo |
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| Přispěvatelé: | Arcozzi N., Domelevo K., Petermichl S. |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Stochastic process Mathematics::Operator Algebras Applied Mathematics General Mathematics Cauchy–Riemann equations Function (mathematics) Singular integral Conditional expectation Singular integrals martingale transforms symbols.namesake Orthogonality symbols Hilbert transform Mathematics Analytic function |
| Popis: | We show that the centered discrete Hilbert transform on integers applied to a function can be written as the conditional expectation of a transform of stochastic integrals, where the stochastic processes considered have jump components. The stochastic representation of the function and that of its Hilbert transform are under differential subordination and orthogonality relation with respect to the sharp bracket of quadratic covariation. This illustrates the Cauchy Riemann relations of analytic functions in this setting. This result is inspired by the seminal work of Gundy and Varopoulos on stochastic representation of the Hilbert transform in the continuous setting. |
| Databáze: | OpenAIRE |
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