Geodesic
One example of a random change of
Teoriâ slučajnyh processov, Tome 13 (2007) no. 3, pp. 12-21.

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We propose a random change of time for a class of generalized di?usion processes such that the corresponding stochastic differential equation (with generalized coe?cients) is transformed into an ordinary one (its coe?cients are some non-generalized functions). It turns out that the latter stochastic differential equation has no property of the (weak) uniqueness of a solution.
Keywords: random change of time, stochastic differential equation, uniqueness of solution.
Mots-clés : Diffusion process 
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Olga V. Aryasova; Mykola I. Portenko. One example of a random change of. Teoriâ slučajnyh processov, Tome 13 (2007) no. 3, pp. 12-21. http://geodesic.mathdoc.fr/item/THSP_2007_13_3_a1/

[1] O. V. Aryasova, M. I. Portenko, “One class of multidimensional stochastic di?erential equations having no property of weak uniqueness of a solution”, Theory Stochast. Process, 11:27 (2005), 14-–28

[2] v. I, II, Acad.Press., Springer, New York, Berlin, 1965

[3] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice–Hall, Englewood Cliffs, N.J., 1964

[4] Amer. Math. Soc., Providence, RI, 1990

[5] N. I. Portenko, “On multidimensional skew Brownian motion and the Feynman–Kac formula”, Theory Stochast. Process., 4:20 (1998), 60–70