{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,16]],"date-time":"2024-04-16T18:17:00Z","timestamp":1713291420605},"reference-count":22,"publisher":"Institute of Mathematical Statistics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Braz. J. Probab. Stat."],"published-print":{"date-parts":[[2019,8,1]]},"DOI":"10.1214\/18-bjps400","type":"journal-article","created":{"date-parts":[[2019,6,10]],"date-time":"2019-06-10T08:04:21Z","timestamp":1560153861000},"source":"Crossref","is-referenced-by-count":3,"title":["Density for solutions to stochastic differential equations with unbounded drift"],"prefix":"10.1214","volume":"33","author":[{"given":"Christian","family":"Olivera","sequence":"first","affiliation":[]},{"given":"Ciprian","family":"Tudor","sequence":"additional","affiliation":[]}],"member":"108","reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"Bally, V. and Caramellino, L. (2017). Regularity of probability laws by using an interpolation method. *Annals of Probability<\/i> ***45<\/b>, 1110\u20131159.","DOI":"10.1214\/15-AOP1082"},{"key":"3","doi-asserted-by":"crossref","unstructured":"Ba\u00f1os, D. and Kr\u00fchner, P. (2017). H\u00f6lder continuous densities of solutions of SDEs with measurable and path dependent drift coefficients. ***Stochastic Processes and Their Applications<\/i> ***127<\/b>, 1785\u20131799.","DOI":"10.1016\/j.spa.2016.09.015"},{"key":"4","doi-asserted-by":"crossref","unstructured":"De Marco, S. (2011). Smoothness and asymptotic estimates of densities for SDEs with locally smooth coefficients and applications to square root-type diffusions. ***The Annals of Applied Probability<\/i> ***21<\/b>, 1282\u20131321.","DOI":"10.1214\/10-AAP717"},{"key":"5","doi-asserted-by":"crossref","unstructured":"Debussche, A. and Fournier, N. (2013). Existence of densities for stable-like driven SDE\u2019s with H\u00f6lder continuous coefficients. ***Journal of Functional Analysis<\/i> ***264<\/b>, 1757\u20131778.","DOI":"10.1016\/j.jfa.2013.01.009"},{"key":"6","doi-asserted-by":"crossref","unstructured":"Flandoli, F., Gubinelli, M. and Priola, E. (2010a). Well-posedness of the transport equation by stochastic perturbation. ***Inventiones Mathematicae<\/i> ***180<\/b>, 1\u201353.","DOI":"10.1007\/s00222-009-0224-4"},{"key":"7","doi-asserted-by":"crossref","unstructured":"Flandoli, F., Gubinelli, M. and Priola, E. (2010b). Flow of diffeomorphisms for SDEs with unbounded H\u00f6lder continuous drift. ***Bulletin Des Sciences Math\u00e9matiques<\/i> ***134<\/b>, 405\u2013422.","DOI":"10.1016\/j.bulsci.2010.02.003"},{"key":"8","unstructured":"Fournier, N. and Printems, J. (2010). Absolute continuity for some one-dimension al processes. ***Bernoulli<\/i> ***16<\/b>, 343\u2013360."},{"key":"9","doi-asserted-by":"crossref","unstructured":"Hayashi, M., Kohatsu-Higa, A. and Yuki, G. (2013). Local H\u00f6lder continuity property of the densities of solutions of SDEs with singular coefficients. ***Journal of Theoretical Probability<\/i> ***26<\/b>, 1117\u20131134.","DOI":"10.1007\/s10959-012-0430-7"},{"key":"10","doi-asserted-by":"crossref","unstructured":"Kohatsu-Higa, A. (2003). Lower bounds for densities of uniformly elliptic random variables on Wiener space. ***Probability Theory and Related Fields<\/i> ***126<\/b>, 421\u2013457.","DOI":"10.1007\/s00440-003-0272-4"},{"key":"11","doi-asserted-by":"crossref","unstructured":"Kohatsu-Higa, A. and Makhlouf, A. (2013). Estimates for the density of functionals of sdes with irregular drift. ***Stochastic Processes and Their Applications<\/i> ***123<\/b>, 1716\u20131728.","DOI":"10.1016\/j.spa.2013.01.006"},{"key":"12","doi-asserted-by":"crossref","unstructured":"Kohatsu-Higa, A. and Tanaka, A. (2012). Malliavin calculus method to study densities of additive functionals of SDE\u2019s with irregular drifts. ***Annales de L\u2019IHP Probabilit\u00e9s et Statistiques<\/i> ***48<\/b>, 871\u2013883.","DOI":"10.1214\/11-AIHP418"},{"key":"13","doi-asserted-by":"crossref","unstructured":"Kunita, H. (1984). Stochastic differential equations and stochastic flows of diffeomorphisms. In ***Ecole D\u2019\u00e9t\u00e9 de Probabilit\u00e9s de Saint-Flour, XII\u20131982. Lecture Notes in Math.<\/i> ***1097<\/b>, 143\u2013303. Berlin: Springer.","DOI":"10.1007\/BFb0099433"},{"key":"15","doi-asserted-by":"crossref","unstructured":"Nourdin, I. and Viens, F. (2009). Density formula and concentration inequalities with Malliavin calculus. ***Electronic Journal of Probability<\/i> ***14<\/b>, 2287\u20132309.","DOI":"10.1214\/EJP.v14-707"},{"key":"17","doi-asserted-by":"crossref","unstructured":"Nualart, D. and Quer-Sardanyons, L. (2009). Gaussian density estimates for solutions to quasi-linear stochastic partial differential equations. ***Stochastic Processes and Their Applications<\/i> ***119<\/b>, 3914\u20133938.","DOI":"10.1016\/j.spa.2009.09.001"},{"key":"18","doi-asserted-by":"crossref","unstructured":"Romito, M. (2016). Time regularity of the densities for the Navier\u2013Stokes equations with noise. ***Journal of Evolution Equations<\/i> ***16<\/b>, 503\u2013518.","DOI":"10.1007\/s00028-015-0310-6"},{"key":"19","unstructured":"Romito, M. (2017). A simple method for the existence of a density for stochastic evolutions with rough coefficients. Preprint. Available at arXiv:1707.05042<\/a>."},{"key":"21","doi-asserted-by":"crossref","unstructured":"Shigekawa, I. (1980). Derivatives of Wiener functionals and absolute continuity of induced measures. ***Journal of Mathematics of Kyoto University<\/i> ***20<\/b>, 263\u2013289.","DOI":"10.1215\/kjm\/1250522278"},{"key":"22","unstructured":"Zhang, X. (2014). Stochastic differential equations with Sobolev diffusion and singular drift. ***The Annals of Applied Probability<\/i> ***26<\/b>, 2697\u20132732."},{"key":"2","doi-asserted-by":"crossref","unstructured":"Bally, V., Caramellino, L. and Cont, R. (2016). Stochastic integration by parts and functional It\u00f4 calculus. In ***Lecture Notes of the Barcelona Summer School on Stochastic Analysis Held in Barcelona, July 23\u201327, 2012. Advanced Courses in Mathematics. CRM Barcelona<\/i> Cham: Birkh\u00e4user\/Springer.","DOI":"10.1007\/978-3-319-27128-6"},{"key":"14","doi-asserted-by":"crossref","unstructured":"Nourdin, I. and Peccati, G. (2012). **Normal Approximations with Malliavin Calculus from Stein\u2019s Method to Universality<\/i>. Cambridge: Cambridge University Press.","DOI":"10.1017\/CBO9781139084659"},{"key":"16","unstructured":"Nualart, D. (2006). **Malliavin Calculus and Related Topics<\/i>, 2nd ed. New York: Springer."},{"key":"20","unstructured":"Sanz-Sol\u00e9, M. (1995). **Malliavin Calculus. With Applications to Stochastic Partial Differential Equations<\/i>. Lausanne: Fundamental Sciences, EPFL Press."}],"container-title":["Brazilian Journal of Probability and Statistics"],"original-title":[],"link":[{"URL":"https:\/\/projecteuclid.org\/download\/pdfview_1\/euclid.bjps\/1560153850","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,16]],"date-time":"2021-04-16T12:55:40Z","timestamp":1618577740000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/brazilian-journal-of-probability-and-statistics\/volume-33\/issue-3\/Density-for-solutions-to-stochastic-differential-equations-with-unbounded-drift\/10.1214\/18-BJPS400.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,1]]},"references-count":22,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,8,1]]}},"URL":"http:\/\/dx.doi.org\/10.1214\/18-bjps400","relation":{},"ISSN":["0103-0752"],"issn-type":[{"value":"0103-0752","type":"print"}],"subject":["Statistics and Probability"],"published":{"date-parts":[[2019,8,1]]}}}*