arXiv subjects

Sharan Srinivasan

Publications and source records attributed to Sharan Srinivasan.

3 recordsLinked to original sources

arXiv2026

The Variational Approach in Filtering and Correlated Noise

The variational formulation of nonlinear filtering due to Mitter and Newton characterizes the filtering distribution as the unique minimizer of a free energy functional involving the relative entropy with respect to the prior and an expected energy. This formulation rests on an absolute continuity condition between the joint path measure and a product reference measure. We prove that this condition necessarily fails whenever the signal and observation diffusions share a common noise source. Specifically we show that the joint and product measures are mutually singular, so no choice of reference measure can salvage the formulation. We then introduce a conditional variational principle that replaces the prior with a reference measure that preserves the noise correlation structure. This generalization recovers the Mitter--Newton formulation as a special case when the noises are independent, and yields an explicit free energy characterization of the filter in the linear correlated-noise setting.

math.PR↗

arXiv2026

Robust Filtering of L\'evy-driven Stochastic Models

We study robust nonlinear filtering for stochastic models driven by L\'evy processes, where the signal and observation processes are coupled through common Brownian and jump noise. Robustness, defined as the continuous dependence of the filter on the observation path, is essential whenever the observation process deviates from the idealized model, for instance when a path must be reconstructed from discrete-time samples. This question is well understood for continuous semimartingale systems but largely open in the presence of jumps. We construct a version of the filter and establish its continuity in two regimes. For processes with finitely many jumps on compact intervals, we prove continuity in both the rough $p$-variation and $p$-variation topologies on cadlag path space, without requiring a separability condition on the jump coefficients. For processes with infinitely many jumps, we prove continuity in a modified rough $p$-variation topology adapted to cadlag geometric rough paths, under an additional separability assumption. In both cases, our approach relies on Stratonovich and Marcus flow decompositions rather than the It\^o-based methods of recent work. The resulting geometric rough-path lifts yield pathwise convergence guarantees and can be constructed directly from discrete observations without knowledge of the underlying probability law.

math.PR↗

arXiv2025

Linear Quadratic Control with Non-Markovian and Non-Semimartingale Noise Models

The standard linear quadratic Gaussian (LQG) framework assumes a Brownian noise process and relies on classical stochastic calculus tools, such as those based on It\^o calculus. In this paper, we solve a generalized linear quadratic optimal control problem where the process and measurement noises can be non-Markovian and non-semimartingale stochastic processes with sample paths that have low H\"older regularity. Since these noise models do not, in general, permit the use of the standard It\^o calculus, we employ rough path theory to formulate and solve the problem. By leveraging signature representations and controlled rough paths, we derive the optimal state estimation and control strategies.

eess.SY↗