{"paper":{"title":"A Guided Tour of the Equations of Nonlinear Filtering for Diffusion Processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fabien Campillo, Myriam Corso","submitted_at":"2026-06-08T09:39:40Z","abstract_excerpt":"These pedagogical notes provide an introduction to nonlinear filtering for diffusion processes. The objective of nonlinear filtering is to estimate an unobserved stochastic state from partial and noisy observations, and thereby characterize the conditional distribution of the state given the observation history. After introducing the state-observation model, we develop the main tools of the theory, including Markov semigroups, infinitesimal generators, and change-of-measure methods. This leads naturally to the Kallianpur-Striebel formula, the Zakai equation for the unnormalized filter, and the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09272","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.09272/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}