arXiv subjects

Andrea Iannucci

Publications and source records attributed to Andrea Iannucci.

3 recordsLinked to original sources

arXiv2026

Pathwise Optimal Control and Rough Fractional Hamilton-Jacobi-Bellman Equations for Rough-Fractional Dynamics

In this work, we investigate the degeneracy problem in pathwise control, extending the framework developed in \cite{allan2020pathwise} to a more general class of driving signals and a broader set of admissible controls. Our approach consists in choosing admissible controls from a suitable class of Hölder-continuous paths. This leads naturally to the use of fractional derivatives and transforms the original control equation into a fractional dynamics system. Within this setting, we derive sufficient conditions ensuring that the control problem remains non-degenerate. We then build on the analysis developed in \cite{gomoyunov2020dynamic,gomoyunov2020theory,gomoyunov2021viscosity} to study the resulting value function and the associated Hamilton--Jacobi--Bellman equation.

math.OC↗

arXiv2026

Nonlinear Stochastic Filtering with Volterra Gaussian noises

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.

math.PR↗

arXiv2026

Signature Kernel and Schwinger-Dyson Kernel Equations as Two-Parameter Rough Differential Equations

We develop a rough-path framework for two-parameter rough differential equations on rectangular and simplicial domains, motivated by the signature kernel and Schwinger--Dyson kernel equations. The theory is formulated in spaces of jointly controlled rough paths and is based on a robust two-parameter rough integration framework. In particular, we introduce a notion of rough integration over two-dimensional simplices at low regularity extending previous results in the literature. Within this setting, we show that the signature kernel equation arises naturally as a two-parameter rough differential equation and establish well-posedness and stability. We also extend the Schwinger--Dyson kernel equation, previously formulated for bounded-variation paths, to rough driving signals, proving existence and uniqueness in appropriate controlled rough path spaces. In the smooth rough path regime, we relate the resulting equations to PDE and integro-differential formulations. Finally, we derive and analyse a numerical scheme for the rough Schwinger--Dyson equation, including runtime and memory complexity estimates, and illustrate its performance with numerical experiments.

math.PR↗