On a martingale characterization of two-parameter Wiener process

Enrique M. Cabaña

Statistics & Probability Letters, 1990, vol. 10, issue 3, 263-270

Abstract: A generalization of martingales, named string-martingales in this paper, is introduced for two-dimensional-parameter processes. The two-parameter standard Wiener process is then characterised as a strong-martingale with continuous paths, and an additional property which states that a sort of quadratic variation of the process is deterministic, and given by the Lebesque measure.

Keywords: Two-parameter; Wiener; process; martingales; vibrating; string; forced; by; noise; string-martingales (search for similar items in EconPapers)
Date: 1990
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