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Linked References

1. R. Azencott, “Behavior of diffusion semi-groups at infinity,” Bulletin de la Société Mathématique de France, vol. 102, pp. 193–240, 1974. View at Zentralblatt MATH · View at MathSciNet
2. R. L. Bishop and R. J. Crittenden, Geometry of Manifolds, vol. 15 of Pure and Applied Mathematics, Academic Press, New York, 1964. View at Zentralblatt MATH · View at MathSciNet
3. K. D. Elworthy, Stochastic Differential Equations on Manifolds, vol. 70 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 1982. View at Zentralblatt MATH · View at MathSciNet
4. M. I. Freidlin and A. D. Wentzell, Random Perturbations of Dynamical Systems, vol. 260 of Fundamental Principles of Mathematical Sciences, Springer, New York, 1984. View at Zentralblatt MATH · View at MathSciNet
5. I. I. Gikhman and A. V. Skorohod, Introduction to the Theory of Random Processes, Nauka, Moscow, 1977. View at Zentralblatt MATH · View at MathSciNet
6. Yu. E. Gliklikh, “On conditions of non-local prolongability of integral curves of vector fields,” Differential equations, vol. 12, no. 4, pp. 743–744, 1977 (Russian).
7. Yu. E. Gliklikh, “A necessary and sufficient condition of completeness for a certain class of stochastic flows on manifolds,” in Trudy seminara po vektornomu i tenzornomu analizu, vol. 26, pp. 130–138, Moscow State University, Moscow, 2005.
8. Yu. E. Gliklikh, Global and Stochastic Analysis in Problems of Mathematical Physics, URSS (KomKniga), Moscow, 2005.
9. Yu. E. Gliklikh, “A necessary and sufficient condition for completeness of stochastic flows continuous at infinity,” Warwick preprint, August 2004, no. 8, pp. 1–7.
10. Yu. E. Gliklikh and L. A. Morozova, “Conditions for global existence of solutions of ordinary differential, stochastic differential, and parabolic equations,” International Journal of Mathematics and Mathematical Sciences, vol. 2004, no. 17–20, pp. 901–912, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
11. Yu. E. Gliklikh and A. V. Sinelnikov, “On a certain necessary and sufficient condition for completeness of a vector field on a Banach manifold,” in Trudy matematicheskogo fakul'teta Voronezhskogo gosudarstvennogo universiteta, no. 9, pp. 46–50, 2005.
12. C. Godbillon, Géométrie différentielle et mécanique analytique, Hermann, Paris, 1969. View at Zentralblatt MATH · View at MathSciNet
13. S. Lang, Differential Manifolds, Springer, New York, 1985. View at Zentralblatt MATH · View at MathSciNet
14. X.-M. Li, “Properties at infinity of diffusion semigroups and stochastic flows via weak uniform covers,” Potential Analysis, vol. 3, no. 4, pp. 339–357, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
15. J.-P. Penot, “Weak topology on functional manifolds,” in Global Analysis and Its Applications (Lectures, Internat. Sem. Course, Internat. Centre Theoret. Phys., Trieste, 1972), vol. 3, pp. 75–84, International Atomic Energy Agency, Vienna, 1974. View at Zentralblatt MATH · View at MathSciNet
16. L. Schwartz, “Processus de Markov et désintégrations régulières,” Université de Grenoble. Annales de l'Institut Fourier, vol. 27, no. 3, pp. xi, 211–277, 1977. View at Zentralblatt MATH · View at MathSciNet
17. L. Schwartz, “Le semi-groupe d'une diffusion en liaison avec les trajectoires,” in Séminaire de Probabilités, XXIII, vol. 1372 of Lecture Notes in Math., pp. 326–342, Springer, Berlin, 1989. View at Zentralblatt MATH · View at MathSciNet