Geodesic
Tightness of Continuous Stochastic Processes
Discussiones Mathematicae. Probability and Statistics, Tome 26 (2006) no. 2, pp. 151-162.

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Some sufficient conditins for tightness of continuous stochastic processes is given. It is verified that in the classical tightness sufficient conditions for continuous stochastic processes it is possible to take a continuous nondecreasing stochastic process instead of a deterministic function one.
Keywords: continuous stochastic processes, weak compactness of sequences of stochastic processes 
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Kisielewicz, Michał. Tightness of Continuous Stochastic Processes. Discussiones Mathematicae. Probability and Statistics, Tome 26 (2006) no. 2, pp. 151-162. http://geodesic.mathdoc.fr/item/DMPS_2006_26_2_a2/

[1] P. Billingsley, Convergence of Probability Measures, John Wiley and Sons, Inc. New York-London-Toronto 1977.

[2] J. Jacod and A. Shiryaev, Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin-Heildelberg-New York 1987.

[3] N. Ikeda and S. Wantanabe, Stochastic Diferential Equation and Diffusion Processes, North Holand Publ., Amsterdam 1981.