{"doi":"10.1002/pamm.201310186","title":"Reachability and Observability Concepts for Stochastic Systems","abstract":"<jats:title>Abstract</jats:title><jats:p>We define observability and reachability and introduce the corresponding Gramians for a Levy driven linear system like Benner, Damm in [3] which focused on the case of Wiener noise. We additionally show that the sets of observable and reachable states are characterized by these Gramians. This is analogous to deterministic systems, where observability and reachability concepts are described in Sections 4.2.1 and 4.2.2 in Antoulas [1]. (© 2013 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)</jats:p>","journal":"PAMM","year":2013,"id":21552,"datarank":0.10397207708399181,"base_score":0.6931471805599453,"endowment":0.6931471805599453,"self_citation_contribution":0.10397207708399181,"citation_network_contribution":0.0,"self_endowment_contribution":0.10397207708399181,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":1,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":138333,"name":"Martin Redmann","orcid":null,"position":1,"is_corresponding":false},{"id":138332,"name":"Peter Benner","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":0.6931471805599453,"endowment":0.6931471805599453,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"21071399","pmcid":null,"openalex_id":"https://openalex.org/W1884874476","authors":[],"funders":[],"total_grants":0,"fwci":0.2496,"citation_percentile":0.54704677,"influential_citations":0,"citation_trend":[{"year":2015,"count":1}],"oa_status":"bronze","license":"http://onlinelibrary.wiley.com/termsAndConditions#vor","oa_locations":[{"url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/pamm.201310186","host_type":"journal"},{"url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/pamm.201310186","host_type":"BRONZE"},{"url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/pamm.201310186","host_type":"publisher"},{"url":"https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fpamm.201310186","host_type":"publisher"},{"url":"https://onlinelibrary.wiley.com/doi/pdf/10.1002/pamm.201310186","host_type":"publisher"},{"url":"https://doi.org/10.1002/pamm.201310186","host_type":"journal"},{"url":"http://hdl.handle.net/11858/00-001M-0000-0024-3E4E-6","host_type":"repository"}],"fields_of_study":["Model Reduction and Neural Networks","Probabilistic and Robust Engineering Design","Control Systems and Identification","Mathematics"],"mesh_terms":[],"keywords":["Observability","Reachability","Observable","Mathematics","Noise (video)","Linear system","Computer science","Applied mathematics","Discrete mathematics","Algorithm","Artificial intelligence","Physics","Mathematical analysis"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-06T16:13:01.517781Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}