{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T15:44:23Z","timestamp":1769874263753,"version":"3.49.0"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2014,2,26]],"date-time":"2014-02-26T00:00:00Z","timestamp":1393372800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2014,6]]},"DOI":"10.1007\/s00332-014-9193-x","type":"journal-article","created":{"date-parts":[[2014,2,25]],"date-time":"2014-02-25T19:02:29Z","timestamp":1393354949000},"page":"383-409","source":"Crossref","is-referenced-by-count":60,"title":["Stochastic Nonlinear Schr\u00f6dinger Equations with Linear Multiplicative Noise: Rescaling Approach"],"prefix":"10.1007","volume":"24","author":[{"given":"Viorel","family":"Barbu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"R\u00f6ckner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deng","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,2,26]]},"reference":[{"key":"9193_CR1","doi-asserted-by":"crossref","first-page":"2494","DOI":"10.1016\/j.jde.2011.07.012","volume":"251","author":"V Barbu","year":"2011","unstructured":"Barbu, V., R\u00f6ckner, M.: On a random scaled porous media equation. J. Differ. Equ. 251, 2494\u20132514 (2011)","journal-title":"J. Differ. Equ."},{"key":"9193_CR2","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1007\/s00205-013-0632-x","volume":"209","author":"V Barbu","year":"2013","unstructured":"Barbu, V., R\u00f6ckner, M.: Stochastic variational inequalities and applications to the total variations flow perturbed by linear multiplicative noise. Arch. Ration. Mech. Anal. 209, 797\u2013834 (2013)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"9193_CR3","doi-asserted-by":"crossref","unstructured":"Barchielli, A., Gregoratti, M.: Quantum Trajectories and Measurements in Continuous Case. The Diffusive Case, Lecture Notes Physics, vol. 782, Springer, Berlin (2009)","DOI":"10.1007\/978-3-642-01298-3"},{"key":"9193_CR4","doi-asserted-by":"crossref","unstructured":"Barchielli, A., Pelegrini, C., Petruccio, F.: Stochastic Schr\u00f6dinger equations with coloured noise. Lett. J. Explor. Front. Phys. EPL 91 (2010)","DOI":"10.1209\/0295-5075\/91\/24001"},{"issue":"2","key":"9193_CR5","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1006\/jfan.1997.3189","volume":"153","author":"AM Cebotarev","year":"1998","unstructured":"Cebotarev, A.M., Fagnola, F.: Sufficient conditions for conservativity of minimal quantum semigroups. J. Funct. Anal. 153(2), 382\u2013401 (1998)","journal-title":"J. Funct. Anal."},{"key":"9193_CR6","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/s002200050672","volume":"205","author":"A Bouard de","year":"1999","unstructured":"de Bouard, A., Debussche, A.: A stochastic nonlinear Schr\u00f6dinger equation via multiplicative noise. Commun. Math. Phys. 205, 161\u2013181 (1999)","journal-title":"Commun. Math. Phys."},{"key":"9193_CR7","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1081\/SAP-120017534","volume":"21","author":"A Bouard de","year":"2003","unstructured":"de Bouard, A., Debussche, A.: The stochastic nonlinear Schr\u00f6dinger equation in $$H^1$$ H 1 . Stoch. Anal. Appl. 21, 97\u2013126 (2003)","journal-title":"Stoch. Anal. Appl."},{"key":"9193_CR8","doi-asserted-by":"crossref","first-page":"1078","DOI":"10.1214\/009117904000000964","volume":"33","author":"A Bouard de","year":"2005","unstructured":"de Bouard, A., Debussche, A.: Blow up for the stochastic nonlinear Schr\u00f6dinger equation with multiplicative noise. Ann. Probab. 33, 1078\u20131110 (2005)","journal-title":"Ann. Probab."},{"key":"9193_CR9","volume-title":"Stochastic Equations in Infinite Dimensions","author":"G Prato Da","year":"2008","unstructured":"Da Prato, G., Zabczyk, J.: Stochastic Equations in Infinite Dimensions. Cambridge University Press, Cambridge, MA (2008)"},{"issue":"2","key":"9193_CR10","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1215\/kjm\/1250519013","volume":"34","author":"S Doi","year":"1994","unstructured":"Doi, S.: On the Cauchy problem for Schr\u00f6dinger type equation and the regularity of solutions. J. Math. Kyoto Univ. 34(2), 319\u2013328 (1994)","journal-title":"J. Math. Kyoto Univ."},{"key":"9193_CR11","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1080\/03605309608821178","volume":"21","author":"S Doi","year":"1996","unstructured":"Doi, S.: Remarks on the Cauchy problem for Schr\u00f6dinger-type equations. Commun. PDE 21, 163\u2013178 (1996)","journal-title":"Commun. PDE"},{"issue":"1","key":"9193_CR12","first-page":"191","volume":"10","author":"F Fagnola","year":"2013","unstructured":"Fagnola, F., Mora, C.M.: Stochastic Schr\u00f6dinger equations and applications to Ehrenfast-type theorems. ALEA. Lat. J. Probab. Math. Stat. 10(1), 191\u2013223 (2013)","journal-title":"ALEA. Lat. J. Probab. Math. Stat."},{"issue":"4","key":"9193_CR13","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1080\/07362994.2011.581091","volume":"29","author":"W Grecksch","year":"2011","unstructured":"Grecksch, W., Lisei, H.: Stochastic nonlinear equations of Schr\u00f6dinger type. Stoch. Anal. Appl. 29(4), 631\u2013653 (2011)","journal-title":"Stoch. Anal. Appl."},{"key":"9193_CR14","doi-asserted-by":"crossref","unstructured":"Kato, T.: Nonliner Schr\u00f6dinger equations, Schr\u00f6dinger operators (S\u00f8nderberg 1988), 218\u2013263. Lecture Notes in Physics, 345, Springer, Berlin (1989)","DOI":"10.1007\/3-540-51783-9_22"},{"key":"9193_CR15","doi-asserted-by":"crossref","unstructured":"Kendal, M., Price, C.J.: Zeros of Brownian polynomials. Stoch. Rep. 70, 3\u20134, 217\u2013308","DOI":"10.1080\/17442500008834255"},{"key":"9193_CR16","unstructured":"Krein, S.G.: Linear Differential Equations in Banach Spaces. Translations of Mathematical Monographs, vol. 29. American Mathematical Society (1972)"},{"key":"9193_CR17","volume-title":"Introduction to Nonlinear Dispersive Equations","author":"F Linares","year":"2009","unstructured":"Linares, F., Ponce, G.: Introduction to Nonlinear Dispersive Equations. Springer, Berlin (2009)"},{"issue":"6","key":"9193_CR18","doi-asserted-by":"crossref","first-page":"1479","DOI":"10.1016\/j.jfa.2008.05.022","volume":"255","author":"J Marzuola","year":"2008","unstructured":"Marzuola, J., Metcalfe, J., Tataru, D.: Strichartz estimates and local smoothing estimates for asymptotically flat Schr\u00f6dinger equations. J. Funct. Anal. 255(6), 1479\u20131553 (2008)","journal-title":"J. Funct. Anal."},{"issue":"2","key":"9193_CR19","first-page":"59","volume":"18","author":"CM Mora","year":"2008","unstructured":"Mora, C.M., Robolledo, R.: Basic properties of nonlinear stochastic Schr\u00f6dinger equation deriven by Brownian motions. Ann. Appl. Probab. 18(2), 59\u2013619 (2008)","journal-title":"Ann. Appl. Probab."},{"key":"9193_CR20","unstructured":"Tataru, D.: Personal Communication"}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-014-9193-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00332-014-9193-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-014-9193-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T23:43:17Z","timestamp":1565221397000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00332-014-9193-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,2,26]]},"references-count":20,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,6]]}},"alternative-id":["9193"],"URL":"https:\/\/doi.org\/10.1007\/s00332-014-9193-x","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,2,26]]}}}