{"id":"https://openalex.org/W1644437411","doi":"https://doi.org/10.1137/140990322","title":"On the Asymptotic Estimates for Exit Probabilities and Minimum Exit Rates of Diffusion Processes Pertaining to a Chain of Distributed Control Systems","display_name":"On the Asymptotic Estimates for Exit Probabilities and Minimum Exit Rates of Diffusion Processes Pertaining to a Chain of Distributed Control Systems","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1644437411","doi":"https://doi.org/10.1137/140990322","mag":"1644437411"},"language":"en","primary_location":{"id":"doi:10.1137/140990322","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140990322","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005744799","display_name":"Getachew K. Befekadu","orcid":"https://orcid.org/0000-0001-5846-4201"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Getachew K. Befekadu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5077171773","display_name":"Panos J. Antsaklis","orcid":"https://orcid.org/0000-0002-6836-5028"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Panos J. Antsaklis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4825,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.81560526,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"53","issue":"4","first_page":"2297","last_page":"2318"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.732150673866272},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6846634149551392},{"id":"https://openalex.org/keywords/diffusion-process","display_name":"Diffusion process","score":0.5355029106140137},{"id":"https://openalex.org/keywords/hitting-time","display_name":"Hitting time","score":0.5277700424194336},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4784948229789734},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.46622326970100403},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.437699556350708},{"id":"https://openalex.org/keywords/large-deviations-theory","display_name":"Large deviations theory","score":0.4218122959136963},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33570486307144165},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13107523322105408}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.732150673866272},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6846634149551392},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.5355029106140137},{"id":"https://openalex.org/C199277547","wikidata":"https://www.wikidata.org/wiki/Q5872687","display_name":"Hitting time","level":2,"score":0.5277700424194336},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4784948229789734},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.46622326970100403},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.437699556350708},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.4218122959136963},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33570486307144165},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13107523322105408},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C56739046","wikidata":"https://www.wikidata.org/wiki/Q192060","display_name":"Knowledge management","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C3017618536","wikidata":"https://www.wikidata.org/wiki/Q304994","display_name":"Innovation diffusion","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140990322","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140990322","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W592153361","https://openalex.org/W1494628843","https://openalex.org/W1513091520","https://openalex.org/W1567262822","https://openalex.org/W1906260424","https://openalex.org/W1968466383","https://openalex.org/W1978187888","https://openalex.org/W1980073551","https://openalex.org/W1992691072","https://openalex.org/W2021268474","https://openalex.org/W2021611402","https://openalex.org/W2028121921","https://openalex.org/W2036807120","https://openalex.org/W2047327648","https://openalex.org/W2048258543","https://openalex.org/W2050912582","https://openalex.org/W2059922898","https://openalex.org/W2061137576","https://openalex.org/W2064791846","https://openalex.org/W2070267857","https://openalex.org/W2073724897","https://openalex.org/W2085482925","https://openalex.org/W2086263802","https://openalex.org/W2160072695","https://openalex.org/W2181351703","https://openalex.org/W2596711886","https://openalex.org/W3099639761"],"related_works":["https://openalex.org/W2479290556","https://openalex.org/W2013381508","https://openalex.org/W4313557736","https://openalex.org/W3015820235","https://openalex.org/W4239935576","https://openalex.org/W2051148294","https://openalex.org/W1537594590","https://openalex.org/W4386135456","https://openalex.org/W4297780587","https://openalex.org/W4383047067"],"abstract_inverted_index":{"In":[0,103],"this":[1],"paper,":[2],"we":[3,105,235,251],"consider":[4,106],"a":[5,10,16,26,81,99,128,133,139,161,165,189,221,228,237,267],"diffusion":[6,84,124,199,262],"process":[7,85,125,200,263],"pertaining":[8],"to":[9,40,71,127,226,266],"distributed":[11,56,179],"control":[12,57,169,180,248,277],"system":[13,58,181],"formed":[14,59],"by":[15,60],"chain":[17,177],"of":[18,155,167,178,230,244,260,269],"$n$":[19],"subsystems":[20,64],"(with":[21],"$n":[22],"\\ge":[23],"2$),":[24],"where":[25],"random":[27,184],"perturbation":[28],"enters":[29],"only":[30],"in":[31,88],"the":[32,41,55,61,67,72,83,89,92,107,118,123,143,153,156,175,192,198,203,209,213,242,245,256,261,275],"first":[33,62,68],"subsystem":[34,69],"and":[35,208],"is":[36,86,98],"then":[37],"subsequently":[38],"transmitted":[39],"other":[42],"subsystems.":[43],"We":[44,112,187],"also":[45,223],"assume":[46],"that,":[47],"for":[48,117,145,164,212,233,255,274],"any":[49],"$\\ell":[50],"\\in":[51],"\\{2,":[52],"\\ldots,":[53],"n\\}$,":[54],"$\\ell$":[63],"(i.e.,":[65],"from":[66,132,202],"up":[70],"$\\ell$th":[73],"subsystem)":[74,130],"satisfies":[75],"an":[76,114,147,253],"appropriate":[77],"H\u00f6rmander":[78],"condition.":[79],"As":[80],"result,":[82],"degenerate,":[87],"sense":[90],"that":[91,171,240],"backward":[93],"operator":[94],"associated":[95,173],"with":[96,121,174,182,196,216,264],"it":[97],"degenerate":[100],"parabolic":[101],"equation.":[102],"particular,":[104],"following":[108],"two":[109],"problems:":[110],"(i)":[111],"provide":[113,236,252],"asymptotic":[115,148],"estimate":[116,149,254],"exit":[119,157,194,258],"probability":[120,158,259],"which":[122,197,234],"(corresponding":[126],"particular":[129],"exits":[131,201],"given":[134,204],"bounded":[135,205],"open":[136,206],"domain":[137,207],"during":[138],"certain":[140],"time":[141],"interval;":[142],"approach":[144],"such":[146],"basically":[150],"relies":[151],"on":[152],"interpretation":[154],"function":[159,163],"as":[160],"value":[162],"family":[166,229],"stochastic":[168],"problems":[170],"are":[172],"underlying":[176],"small":[183],"perturbations.":[185],"(ii)":[186],"establish":[188],"connection":[190,222],"between":[191],"minimum":[193],"rate":[195],"principal":[210],"eigenvalue":[211],"infinitesimal":[214],"generator":[215],"zero":[217],"boundary":[218],"conditions.":[219],"Such":[220],"allows":[224],"us":[225],"derive":[227],"Hamilton--Jacobi--Bellman":[231],"equations":[232],"verification":[238],"theorem":[239],"shows":[241],"validity":[243],"corresponding":[246],"optimal":[247,271,276],"problems.":[249,278],"Moreover,":[250],"attainable":[257],"respect":[265],"set":[268],"admissible":[270],"Markov":[272],"controls":[273]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
