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1. P. Kotelenez, “A stochastic Navier-Stokes equation for the vorticity of a two-dimensional fluid,” The Annals of Applied Probability, vol. 5, no. 4, pp. 1126–1160, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
2. C. Marchioro and M. Pulvirenti, “Hydrodynamics in two dimensions and vortex theory,” Communications in Mathematical Physics, vol. 84, no. 4, pp. 483–503, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
3. A. Amirdjanova, Topics in stochastic fluid dynamics: a vorticity approach, Ph.D. thesis, University of North Carolina at Chapel Hill, 2000.
4. A. Amirdjanova, “Vortex theory approach to stochastic hydrodynamics,” Mathematical and Computer Modelling, vol. 45, no. 11-12, pp. 1319–1341, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
5. A. Amirdjanova and J. Xiong, “Large deviation principle for a stochastic Navier-Stokes equation in its vorticity form for a two-dimensional incompressible flow,” Discrete and Continuous Dynamical Systems. Series B, vol. 6, no. 4, pp. 651–666, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
6. A. J. Chorin, “Numerical study of slightly viscous flow,” Journal of Fluid Mechanics, vol. 57, no. 4, pp. 785–796, 1973. View at Publisher · View at Google Scholar
7. J. B. Walsh, “An introduction to stochastic partial differential equations,” in École d'Été de Probabilités de Saint-Flour, XIV—1984, vol. 1180 of Lecture Notes in Math., pp. 265–439, Springer, Berlin, Germany, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
8. P. Kotelenez, Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic equations, vol. 58 of Stochastic Modelling and Applied Probability, Springer, New York, NY, USA, 2008.
9. P. M. Kotelenez and T. G. Kurtz, “Macroscopic limits for stochastic partial differential equations of McKean-Vlasov type,” Probability Theory and Related Fields, vol. 146, no. 1-2, pp. 189–222, 2010. View at Publisher · View at Google Scholar
10. S. Asakura and F. Oosawa, “On interaction between two bodies immersed in a solution of macromolecules,” The Journal of Chemical Physics, vol. 22, no. 7, pp. 1255–1256, 1954.
11. P. Kotelenez, M. J. Leitman, and J. A. Mann, “Correlated Brownian motions and the depletion effect in colloids,” Journal of Statistical Mechanics: Theory and Experiment, vol. 2009, no. 1, Article ID P01054, 2009. View at Publisher · View at Google Scholar
12. R. M. Dudley, Real Analysis and Probability, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, Calif, USA, 1989.
13. A. de Acosta, “Invariance principles in probability for triangular arrays of $B$-valued random vectors and some applications,” The Annals of Probability, vol. 10, no. 2, pp. 346–373, 1982. View at Publisher · View at Google Scholar
14. P. Kotelenez and B. Seadler, “On the Hahn-Jordan decomposition for signed measure valued stochastic partial differential equations,” to appear in Stochastics and Dynamics.
15. M. Métivier and J. Pellaumail, Stochastic Integration, Academic Press, New York, NY, USA, 1980, Probability and Mathematical Statistics.