Abstract:This article investigates the structural properties of stochastic processes relative to a generalized single jump filtration, extending the framework introduced by A.A. Gushchin (2020) to the case of a non-trivial initial $\sigma$-algebra $\mathscr{H}$. By leveraging the general theory of processes and optional projection techniques, we establish fundamental measurability criteria for random variables and a complete characterization of stopping times and adapted processes. Furthermore, we derive comprehensive martingale and local martingale criteria, providing necessary and sufficient conditions for the preservation of the martingale property in this extended setting.
From: Assylliya Zhunussova [view email]
[v1]
Tue, 2 Jun 2026 21:49:46 UTC (19 KB)
[v2]
Tue, 30 Jun 2026 13:20:15 UTC (17 KB)
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