 Guided smoothing and control for diffusion processesOskar Eklund, Annika Lang and Moritz Schauer Stochastic Processes and their Applications, 2026, vol. 192, issue C Abstract: The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the theory of enlargement of filtrations to show that the conditional process has an additional drift term derived from the backward filtering distribution that is moving or guiding the process towards the observations. This term is intractable, but its effect can be equally introduced by replacing it with a heuristic, where importance weights correct for the discrepancy. From this Markov Chain Monte Carlo and sequential Monte Carlo algorithms are derived to sample from the smoothing distribution. The choice of the guiding heuristic is discussed from an optimal control perspective and evaluated. The results are tested numerically on a stochastic differential equation for reaction–diffusion. Keywords: Stochastic differential equation; Smoothing; Guided process; Enlargement of filtration; Reaction–diffusion; Hamilton–Jacobi–Bellman equation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:192:y:2026:i:c:s0304414925002509 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2025.104806 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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