{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:38:53Z","timestamp":1787326733300,"version":"build-2736575974"},"reference-count":37,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Finan. Math."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>In this paper we derive a scaling limit for an infinite-dimensional limit order book model driven by Hawkes random measures. The dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator. With our choice of scaling the dynamics converges to a coupled SDE-ODE system where limiting best bid and ask price processes follows a diffusion dynamics, the limiting volume density functions follows an ODE in a Hilbert space, and the limiting order arrival and cancellation intensities follow a Volterra--Fredholm integral equation.<\/jats:p>","DOI":"10.1137\/17m1148682","type":"journal-article","created":{"date-parts":[[2019,4,16]],"date-time":"2019-04-16T11:41:02Z","timestamp":1555414862000},"page":"350-393","source":"Crossref","is-referenced-by-count":21,"title":["A Scaling Limit for Limit Order Books Driven by Hawkes Processes"],"prefix":"10.1137","volume":"10","author":[{"given":"Ulrich","family":"Horst","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,4,16]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1142\/S0219024913500258"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/15M1011469"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1142\/S2382626615500057"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1080\/14697688.2014.897000"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1214\/16-AAP1265"},{"key":"atypb6","first-page":"637","author":"Bayraktar E.","year":"2008","journal-title":"New York"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1995.tb05192.x"},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"P. Billingsley,\n                      Convergence of Probability Measures\n                      , Wiley, New York, 1999.","DOI":"10.1002\/9780470316962"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jedc.2015.05.004"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1080\/14697688.2010.539249"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/110856605"},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"C. Corduneanu,\n                      Integral Equations and Applications\n                      , Cambridge University Press, Cambridge, 1991.","DOI":"10.1017\/CBO9780511569395"},{"key":"atypb13","unstructured":"C. Dellacherie and P. A. Meyer,\n                      Probabilities and Potential\n                      , North-Holland, Amsterdam, 1982."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1017\/S0021900200099344"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1017\/S0269964816000413"},{"key":"atypb16","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1111\/j.2517-6161.1971.tb01530.x","volume":"33","author":"Hawkes A. G.","year":"1971","journal-title":"J. Roy. Statist. Soc. Ser. B"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/58.1.83"},{"key":"atypb18","first-page":"6","author":"Hewlett P.","year":"2006","journal-title":"France"},{"key":"atypb19","unstructured":"U. Horst and D. Kreher,\n                      A diffusion approximation for limit order books\n                      , Stochastic Process. Appl., to appear."},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-018-0373-7"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1137\/15M1024226"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2017.0848"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2014.982278"},{"key":"atypb24","unstructured":"F. Hubalek, P. Kr\u00fchner, and T. Rheinl\u00e4nder,\n                      Brownian Trading Excursions and Avalanches\n                      ,https:\/\/arxiv.org\/abs\/1701.00993v1(2017)."},{"key":"atypb25","unstructured":"N. Ikeda and S. Watanabe,\n                      Stochastic Differential Equations and Diffusion Processes\n                      , North-Holland, Amsterdam, 1989."},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1214\/14-AAP1005"},{"key":"atypb27","unstructured":"I. Karatzas and S. Shreve,\n                      Brownian Motion and Stochastic Calculus\n                      , Springer, Berlin, 1991."},{"key":"atypb28","first-page":"746","volume":"4","author":"Keller-Ressel M.","year":"2016","journal-title":"Stoch. Partial Differ. Equ. Anal. Comput."},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1287\/stsy.2017.0005"},{"key":"atypb30","doi-asserted-by":"crossref","unstructured":"P. Lakner, J. Reed, and S. Stoikov,\n                      High frequency asymptotics for the limit order book\n                      , Market Microstruct. Liquid., 2016.","DOI":"10.1142\/S2382626616500040"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1080\/14697688.2017.1403142"},{"key":"atypb32","first-page":"228","volume":"1","author":"Ogata Y.","year":"1988","journal-title":"J. Amer. Statist. Assoc."},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1080\/14697688.2016.1260759"},{"key":"atypb34","doi-asserted-by":"crossref","unstructured":"D. Revuz and M. Yor,\n                      Continuous Martingales and Brownian Motion\n                      , Springer, Berlin, 1999.","DOI":"10.1007\/978-3-662-06400-9"},{"key":"atypb35","first-page":"265","author":"Walsh J.","year":"1986","journal-title":"Berlin"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1215\/kjm\/1250523321"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1137\/130912980"}],"container-title":["SIAM Journal on Financial Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1148682","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:35:22Z","timestamp":1787322922000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1148682"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":37,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/17M1148682"],"URL":"https:\/\/doi.org\/10.1137\/17m1148682","relation":{},"ISSN":["1945-497X"],"issn-type":[{"value":"1945-497X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}