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(2003). <i>Stochastic Differential Equations<\/i>: <i>An Introduction with Applications<\/i>. Springer, Berlin."},{"key":"34","doi-asserted-by":"crossref","unstructured":"[34] Pope, S. B. (2000). <i>Turbulent Flows<\/i>. Cambridge Univ. Press, Cambridge.","DOI":"10.1017\/CBO9780511840531"},{"key":"38","doi-asserted-by":"crossref","unstructured":"[38] Villani, C. (2009). <i>Optimal Transport. Old and New. Grundlehren der Mathematischen Wissenschaften<\/i> [<i>Fundamental Principles of Mathematical Sciences<\/i>] <b>338<\/b>. Springer, Berlin.","DOI":"10.1007\/978-3-540-71050-9"},{"key":"1","doi-asserted-by":"publisher","unstructured":"[1] Baldi, P. (1986). Large deviations and functional iterated logarithm law for diffusion processes. <i>Probab. Theory Related Fields<\/i> <b>71<\/b> 435\u2013453.","DOI":"10.1007\/BF01000215"},{"key":"2","doi-asserted-by":"publisher","unstructured":"[2] Baldi, P., Ben Arous, G. and Kerkyacharian, G. (1992). 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