Abstract:We develop a nonlinear filtering theory for signal-observation systems driven by Volterra Gaussian processes, covering both the Young and genuinely rough regimes. The dynamics are formulated as a rough differential equation in which the observation has a signal-dependent Volterra drift, a structure naturally induced by an equivalent change of measure. We establish global well-posedness of the coupled system and derive a Kallianpur-Striebel formula. We then obtain a robust pathwise representation of the filter. In the one-dimensional setting, we characterise the unnormalised conditional density through a rough Zakai equation and establish its well-posedness using an extension of the rough viscosity framework. Finally, under a partial Hörmander-type condition, we prove that the conditional distribution of the signal admits a smooth density.
From: Andrea Iannucci [view email]
[v1]
Wed, 11 Jun 2025 11:52:19 UTC (59 KB)
[v2]
Sun, 6 Jul 2025 17:12:36 UTC (59 KB)
[v3]
Tue, 25 Aug 2026 12:02:43 UTC (80 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。