{"id":"https://openalex.org/W7151584100","doi":"https://doi.org/10.48550/arxiv.2604.03794","title":"Bounding Transient Moments for a Class of Stochastic Reaction Networks Using Kolmogorov's Backward Equation","display_name":"Bounding Transient Moments for a Class of Stochastic Reaction Networks Using Kolmogorov's Backward Equation","publication_year":2026,"publication_date":"2026-04-04","ids":{"openalex":"https://openalex.org/W7151584100","doi":"https://doi.org/10.48550/arxiv.2604.03794"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.03794","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.03794","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.03794","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049888886","display_name":"Takeyuki Iwasaki","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Iwasaki, Takeyuki","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5012594690","display_name":"Yutaka Hori","orcid":"https://orcid.org/0000-0002-3253-4985"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hori, Yutaka","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5049888886"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.904699981212616,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.904699981212616,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T13052","display_name":"Molecular Communication and Nanonetworks","score":0.026499999687075615,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.019200000911951065,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.7239999771118164},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.6830000281333923},{"id":"https://openalex.org/keywords/moment-closure","display_name":"Moment closure","score":0.6371999979019165},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5734999775886536},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.5388000011444092},{"id":"https://openalex.org/keywords/transient","display_name":"Transient (computer programming)","score":0.5181999802589417},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5131999850273132},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.4991999864578247},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4528999924659729}],"concepts":[{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.7239999771118164},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.6830000281333923},{"id":"https://openalex.org/C2778513689","wikidata":"https://www.wikidata.org/wiki/Q6897109","display_name":"Moment closure","level":3,"score":0.6371999979019165},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6319000124931335},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5734999775886536},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.5388000011444092},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.5181999802589417},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5131999850273132},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5113000273704529},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.4991999864578247},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4528999924659729},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.44620001316070557},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.42239999771118164},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.4101000130176544},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.3874000012874603},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.382999986410141},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3517000079154968},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.3515999913215637},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.34880000352859497},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.33660000562667847},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.33480000495910645},{"id":"https://openalex.org/C34146451","wikidata":"https://www.wikidata.org/wiki/Q5048094","display_name":"Cascade","level":2,"score":0.31279999017715454},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.31200000643730164},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29919999837875366},{"id":"https://openalex.org/C61062188","wikidata":"https://www.wikidata.org/wiki/Q835065","display_name":"Second moment of area","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.273499995470047},{"id":"https://openalex.org/C2777317252","wikidata":"https://www.wikidata.org/wiki/Q18393516","display_name":"Rare events","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.03794","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.03794","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.03794","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.03794","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Stochastic":[0],"chemical":[1],"reaction":[2,169],"networks":[3],"(SRNs)":[4],"in":[5],"cellular":[6],"systems":[7],"are":[8],"commonly":[9],"modeled":[10],"as":[11],"continuous-time":[12],"Markov":[13],"chains":[14],"(CTMCs)":[15],"describing":[16],"the":[17,62,72,74,78,82,88,94,100,103,114,117,152,161,168],"dynamics":[18],"of":[19,26,39,71,81,96,116,139,159],"molecular":[20],"copy":[21,28],"numbers.":[22],"The":[23,133],"exact":[24],"evaluation":[25,138],"transient":[27,58,131],"number":[29],"statistics":[30],"is,":[31],"however,":[32],"often":[33],"hindered":[34],"by":[35,92,146],"a":[36,47,68,122,172],"non-closed":[37],"hierarchy":[38],"moment":[40,89,140],"equations.":[41],"In":[42],"this":[43,109],"paper,":[44],"we":[45],"propose":[46],"method":[48],"for":[49,77,156,177],"computing":[50,178],"theoretically":[51],"guaranteed":[52],"upper":[53],"and":[54,174],"lower":[55],"bounds":[56,129,141],"on":[57,61,102,130],"moments":[59],"based":[60],"Kolmogorov's":[63],"backward":[64],"equation,":[65],"which":[66],"provides":[67,128],"dual":[69,85,110],"representation":[70],"CME,":[73],"governing":[75],"equation":[76],"probability":[79],"distribution":[80],"CTMC.":[83],"This":[84],"formulation":[86],"avoids":[87],"closure":[90],"problem":[91],"shifting":[93],"source":[95],"infinite":[97],"dimensionality":[98],"to":[99,121],"dependence":[101],"initial":[104,144],"state.":[105],"We":[106],"show":[107],"that,":[108],"formulation,":[111],"combined":[112],"with":[113],"monotonicity":[115],"CTMC":[118],"generator,":[119],"leads":[120],"finite-dimensional":[123],"linear":[124],"time-invariant":[125],"system":[126,135],"that":[127],"moments.":[132],"resulting":[134],"enables":[136],"efficient":[137],"across":[142],"multiple":[143],"conditions":[145],"simple":[147],"inner-product":[148],"operations":[149],"without":[150],"recomputing":[151],"bounding":[153,162],"system.":[154],"Further,":[155],"certain":[157],"classes":[158],"SRNs,":[160],"ODEs":[163],"admit":[164],"explicit":[165],"construction":[166],"from":[167],"model,":[170],"providing":[171],"systematic":[173],"constructive":[175],"framework":[176],"provable":[179],"bounds.":[180]},"counts_by_year":[],"updated_date":"2026-04-08T06:07:18.267832","created_date":"2026-04-08T00:00:00"}
