{"id":"https://openalex.org/W4414450511","doi":"https://doi.org/10.48550/arxiv.2508.20883","title":"Lattice Random Walk Discretisations of Stochastic Differential Equations","display_name":"Lattice Random Walk Discretisations of Stochastic Differential Equations","publication_year":2025,"publication_date":"2025-08-28","ids":{"openalex":"https://openalex.org/W4414450511","doi":"https://doi.org/10.48550/arxiv.2508.20883"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2508.20883","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2508.20883","pdf_url":"https://arxiv.org/pdf/2508.20883","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2508.20883","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061125105","display_name":"Samuel Duffield","orcid":"https://orcid.org/0000-0002-8656-8734"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Duffield, Samuel","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029203860","display_name":"Maxwell Aifer","orcid":"https://orcid.org/0000-0003-1936-0877"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aifer, Maxwell","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023223508","display_name":"Denis Melanson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Melanson, Denis","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114439137","display_name":"Zach Belateche","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Belateche, Zach","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5088973719","display_name":"Patrick J. Coles","orcid":"https://orcid.org/0000-0001-9879-8425"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Coles, Patrick J.","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5061125105"],"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.44839999079704285,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.44839999079704285,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.4334999918937683,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.4072999954223633,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.6453999876976013},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.6370999813079834},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5795999765396118},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5153999924659729},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.46889999508857727},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.44600000977516174},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4401000142097473},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.41339999437332153},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.3944000005722046}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7149999737739563},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6453999876976013},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.6370999813079834},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5795999765396118},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5153999924659729},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.46889999508857727},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.44600000977516174},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44190001487731934},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4401000142097473},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.41339999437332153},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3944000005722046},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.38670000433921814},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.37709999084472656},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.3675999939441681},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3463999927043915},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.34630000591278076},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.3248000144958496},{"id":"https://openalex.org/C154072304","wikidata":"https://www.wikidata.org/wiki/Q5747218","display_name":"Heterogeneous random walk in one dimension","level":3,"score":0.3206000030040741},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.3147999942302704},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.290800005197525},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.2856000065803528},{"id":"https://openalex.org/C20353970","wikidata":"https://www.wikidata.org/wiki/Q1056998","display_name":"Simple random sample","level":3,"score":0.2822999954223633},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2808000147342682},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.27869999408721924}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2508.20883","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2508.20883","pdf_url":"https://arxiv.org/pdf/2508.20883","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:doi:10.48550/arxiv.2508.20883","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2508.20883","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2508.20883","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":"pmh:oai:arXiv.org:2508.20883","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2508.20883","pdf_url":"https://arxiv.org/pdf/2508.20883","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"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":{"We":[0,87],"introduce":[1],"a":[2,39,71],"lattice":[3],"random":[4,34],"walk":[5],"discretisation":[6],"scheme":[7],"for":[8],"stochastic":[9,54],"differential":[10],"equations":[11],"(SDEs)":[12],"that":[13,57],"samples":[14],"binary":[15],"or":[16,31],"ternary":[17],"increments":[18],"at":[19],"each":[20],"step,":[21],"suppressing":[22],"complex":[23],"drift":[24],"and":[25,47,82,91],"diffusion":[26,102],"computations":[27],"to":[28,79],"simple":[29],"1":[30],"2":[32],"bit":[33],"values.":[35],"This":[36],"approach":[37],"is":[38],"significant":[40],"departure":[41],"from":[42],"traditional":[43],"floating":[44],"point":[45],"discretisations":[46],"offers":[48],"several":[49],"advantages;":[50],"including":[51,100],"compatibility":[52],"with":[53],"computing":[55],"architectures":[56],"avoid":[58],"floating-point":[59],"arithmetic":[60],"in":[61],"place":[62],"of":[63,70,74,84],"directly":[64],"manipulating":[65],"the":[66,93],"underlying":[67],"probability":[68],"distribution":[69],"bitstream,":[72],"elimination":[73],"Gaussian":[75],"sampling":[76],"requirements,":[77],"robustness":[78],"quantisation":[80],"errors,":[81],"handling":[83],"non-Lipschitz":[85],"drifts.":[86],"prove":[88],"weak":[89],"convergence":[90],"demonstrate":[92],"advantages":[94],"through":[95],"experiments":[96],"on":[97],"various":[98],"SDEs,":[99],"state-of-the-art":[101],"models.":[103]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
