Geodesic
Discrete time approximation of coalescing stochastic flows on the real line
Teoriâ slučajnyh processov, Tome 17 (2011) no. 1, pp. 70-78.

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We have constructed an approximation for the Harris and Arratia flows using a sequence of independent stationary Gaussian processes as a perturbation. We have established which relationship should be between the step of approximation and the smoothness of the covariance of perturbing processes in order that the approximating functions converge to the Arratia flow.
Keywords: Stochastic flow, stochastic differential equation, numerical approximation. 
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I. I. Nishchenko. Discrete time approximation of coalescing stochastic flows on the real line. Teoriâ slučajnyh processov, Tome 17 (2011) no. 1, pp. 70-78. http://geodesic.mathdoc.fr/item/THSP_2011_17_1_a7/

[1] D. F. Kuznetsov, Stochastic Differential Equations: Theory and Practice of Numerical Analysis, Polytechnic Univ., Saint-Petersburg, 2010 (in Russian)

[2] B. Tsirelson, “Nonclassical stochastic flows and continuous products”, Probab. Surv., 1 (2004), 173–298

[3] T. E. Harris, “Coalescing and noncoalescing stochastic flows in ${\mathbb R}_1$”, Stoch. Process. and Their Applic., 17 (1984), 187–210

[4] O. Kallenberg, Foundations of Modern Probability, Springer, New York, 1997

[5] Y. Le Jan, O. Raimond, “Flows, coalescence and noise”, Ann. Probab., 32 (2004), 1247–1315

[6] P. Kotelenez, “A class of quasilinear stochastic partial differential equation of McKean–Vlasov type with mass conservation”, Probab. Th. Relat. Fields, 102 (1995), 159–188

[7] A. A. Dorogovtsev, Measure-Valued Processes and Stochastic Flows, Institute of Math., Kiev, 2007 (in Russian)

[8] A. A. Dorogovtsev, “One Brownian stochastic flow”, Th. Stoch. Proc., 10 (2004), 21–25

[9] P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968

[10] A. A. Dorogovtsev, O. V. Ostapenko, “Large deviations for flows of interacting Brownian motions”, Stochastics and Dynamics, 10:3 (2010), 315–339