{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T19:44:31Z","timestamp":1743018271520,"version":"3.40.3"},"publisher-location":"Cham","reference-count":14,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319684444"},{"type":"electronic","value":"9783319684451"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-68445-1_55","type":"book-chapter","created":{"date-parts":[[2017,10,23]],"date-time":"2017-10-23T20:40:36Z","timestamp":1508791236000},"page":"470-476","source":"Crossref","is-referenced-by-count":2,"title":["A Stochastic Look at Geodesics on the Sphere"],"prefix":"10.1007","author":[{"given":"Marc","family":"Arnaudon","sequence":"first","affiliation":[]},{"given":"Jean-Claude","family":"Zambrini","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,10,24]]},"reference":[{"key":"55_CR1","series-title":"Encyclopaedia of Mathematical Sciences","first-page":"177","volume-title":"Dynamical Systems IV","author":"BA Dubrovin","year":"1990","unstructured":"Dubrovin, B.A., Krichever, J.M., Novikov, S.P.: Integrable systems I. In: Arnold, V.I., Novikov, S.P. (eds.) Dynamical Systems IV. Encyclopaedia of Mathematical Sciences, vol. 4, pp. 177\u2013332. Springer, Heidelberg (1990)"},{"key":"55_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4350-2","volume-title":"Applications of Lie Groups to Differential Equations","author":"P Olver","year":"1993","unstructured":"Olver, P.: Applications of Lie Groups to Differential Equations, 2nd edn. Springer, New York (1993)","edition":"2"},{"unstructured":"It\u00f4, K.: The Brownian motion and tensor fields on a Riemannian manifold. In: Proceedings of the International Congress Mathematical (Stockholm), pp. 536\u2013539 (1962)","key":"55_CR3"},{"key":"55_CR4","volume-title":"Controlled Markov Processes and Viscosity Solutions","author":"WH Fleming","year":"2005","unstructured":"Fleming, W.H., Soner, H.M.: Controlled Markov Processes and Viscosity Solutions, 2nd edn. Springer, New York (2005)","edition":"2"},{"key":"55_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-15074-6","volume-title":"Stochastic Analysis","author":"P Malliavin","year":"1997","unstructured":"Malliavin, P.: Stochastic Analysis. Springer, Heidelberg (1997)"},{"key":"55_CR6","first-page":"243","volume":"22","author":"R Kuwabara","year":"1977","unstructured":"Kuwabara, R.: On the symmetry algebra of the Schr\u00f6dinger wave equation. Math. Japonica 22, 243 (1977)","journal-title":"Math. Japonica"},{"unstructured":"L\u00e9onard, C., Zambrini, J.-C.: Stochastic deformation of Jacobi\u2019s integrability Theorem in Hamiltonian mechanics. Preparation","key":"55_CR7"},{"doi-asserted-by":"crossref","unstructured":"Zambrini, J.-C.: Probability and quantum symmetries in a riemannian manifold. Prog. Probab. 45 (1999). Birkh\u00e4user","key":"55_CR8","DOI":"10.1007\/978-3-0348-8681-9_20"},{"key":"55_CR9","first-page":"461","volume-title":"Stochastic Analysis and Applications: Abel Symposium","author":"T Kolsrud","year":"2005","unstructured":"Kolsrud, T.: Quantum and classical conserved quantities: martingales, conservation law and constants of motion. In: Benth, F.E., Di Nunno, G., Lindstr\u00f8m, T., \u00d8ksendal, B., Zhang, T. (eds.) Stochastic Analysis and Applications: Abel Symposium, pp. 461\u2013491. Springer, Heidelberg (2005)"},{"doi-asserted-by":"crossref","unstructured":"Zambrini, J.-C.: The research program of Stochastic Deformation (with a view toward Geometric Mechanics). In: Dalang, R., Dozzi, M., Flandoli, F., Russo, F. (eds.) Birkh\u00e4userStochastic Analysis, A Series of Lectures (2015)","key":"55_CR10","DOI":"10.1007\/978-3-0348-0909-2_13"},{"doi-asserted-by":"crossref","unstructured":"L\u00e9onard, C.: A survey of the Schr\u00f6dinger problem and some of its connections with optimal transport. Discrete Contin. Dyn. Syst. A 34(4) (2014)","key":"55_CR11","DOI":"10.3934\/dcds.2014.34.1533"},{"key":"55_CR12","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1214\/13-PS220","volume":"11","author":"C L\u00e9onard","year":"2014","unstructured":"L\u00e9onard, C., Roelly, S., Zambrini, J.-C.: Reciprocal processes. A measure-theoretical point of view. Probab. Surv. 11, 237\u2013269 (2014)","journal-title":"Probab. Surv."},{"unstructured":"Arnold, V.: M\u00e9thodes Math\u00e9matiques de la M\u00e9canique Classique. Mir, Moscou (1976)","key":"55_CR13"},{"key":"55_CR14","series-title":"Grundlehren der mathematischen Wissenschaften","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-71050-9","volume-title":"Optimal Transport, Old and New","author":"C Villani","year":"2009","unstructured":"Villani, C.: Optimal Transport, Old and New. Grundlehren der mathematischen Wissenschaften. Springer, Heidelberg (2009)"}],"container-title":["Lecture Notes in Computer Science","Geometric Science of Information"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-68445-1_55","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,4]],"date-time":"2019-10-04T21:58:48Z","timestamp":1570226328000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-68445-1_55"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319684444","9783319684451"],"references-count":14,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-68445-1_55","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]}}}