On the $\varphi$-asymptotic behaviour of solutions of stochastic differential equations
Teoriâ slučajnyh processov, Tome 14 (2008) no. 1, pp. 11-29.

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V. V. Buldygin; O. I. Klesov; J. G. Steinebach; O. A. Tymoshenko. On the $\varphi$-asymptotic behaviour of solutions of stochastic differential equations. Teoriâ slučajnyh processov, Tome 14 (2008) no. 1, pp. 11-29. http://geodesic.mathdoc.fr/item/THSP_2008_14_1_a2/

[1] V. G. Avakumović, “Über einen O–Inversionssatz”, Bull. Int. Acad. Youg. Sci., 29–30 (1936), 107-–117

[2] S. M. Berman, “Sojourns and extremes of a diffusion process on a fixed interval”, Adv. Appl. Prob., 14 (1982), 811-–832 | DOI | MR | Zbl

[3] S. M. Berman, “The tail of the convolution of densities and its application to a model of HIVlatency time”, Ann. Appl. Prob., 2 (1992), 481-–502 | DOI | MR | Zbl

[4] N. H. Bingham, C. M. Goldie, J. L. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1987 | MR | Zbl

[5] V. V. Buldygin, O. I. Klesov, J. G. Steinebach, “Properties of a subclass of Avakumović functions and their generalized inverses”, Ukrain. Math. J., 54 (2002), 179-–206 | DOI | MR | Zbl

[6] Theory Probab. Math. Statist., 70 (2005), 11-–28 | DOI | Zbl

[7] Theory Probab. Math. Statist., 71 (2005), 37-–52 | DOI | MR

[8] Theory Probab. Math. Statist., 72 (2006), 11-–25 | DOI | MR | Zbl

[9] V. V. Buldygin, O. I. Klesov, J. G. Steinebach, “PRV property and the asymptotic behaviour of solutions of stochastic differential equations”, Theory Stoch. Process., 11:27 (2005), 42-–57 | MR | Zbl

[10] V. V. Buldygin, O. I. Klesov, J. G. Steinebach, “On some extensions of Karamata’s theory and their applications”, Publ. Inst. Math. (Beograd) (N. S.), 80(94), 2006, 59-–96 | DOI | MR | Zbl

[11] V. V. Buldygin, O. I. Klesov, J. G. Steinebach, “PRV property and the $\varphi$–Asymptotic behaviour of solutions of stochastic differential equations”, Lithuanian Math. J., 2007, no. 4, 1-–21 | MR

[12] V. V. Buldygin, O. A. Tymoshenko, “On the asymptotic stability of stochastic differential equations”, Naukovi Visti NTUU “KPI”, 2007, no. 1, 126–129

[13] D. B. H. Cline, “Intermediate regular and $\Pi$-variation”, Proc. London Math. Soc., 68, 1994, 594–-616 | DOI | MR | Zbl

[14] D. Djurčić, “O-regularly varying functions and strong asymptotic equivalence”, J. Math. Anal. Appl., 220 (1998), 451-–461 | DOI | MR | Zbl

[15] D. Djurčić, A. Torgašev, “Strong asymptotic equivalence and inversion of functions in the class $K_c$”, J. Math. Anal. Appl., 255 (2001), 383-–390 | DOI | MR | Zbl

[16] I. I. Gihman, A. V. Skorohod, Stochastic Differential Equations, Springer-Verlag, Berlin-Heidelberg-New York, 1972 | MR | Zbl

[17] J. Karamata, “Sur un mode de croissance régulière des fonctions”, Mathematica (Cluj), 4 (1930), 38–-53 | Zbl

[18] J. Karamata, “Bemerkung über die vorstehende Arbeit des Herrn Avakumović, mit näherer Betrachtung einer Klasse von Funktionen, welche bei den Inversionssätzen vorkommen”, Bull. Int. Acad. Youg. Sci., 29–30 (1936), 117-–123

[19] G. Keller, G. Kersting, U. Rösler, “On the asymptotic behaviour of solutions of stochastic differential equations”, Z.Wahrsch. Verw. Geb., 68 (1984), 163-–184 | DOI | MR

[20] O. Klesov, Z. Rychlik, J. Steinebach, “Strong limit theorems for general renewal processes”, Theory Probab. Math. Statist., 21 (2001), 329-–349 | MR | Zbl

[21] B. H. Korenblyum, “On the asymptotic behaviour of Laplace integrals near the boundary of a region of convergence”, Dokl. Akad. Nauk. USSR (N.S.), 109 (1956), 173-–176 | MR

[22] W. Matuszewska, “On a generalization of regularly increasing functions”, Studia Math., 24 (1964), 271-–279 | DOI | MR | Zbl

[23] W. Matuszewska, W. Orlicz, “On some classes of functions with regard to their orders of growth”, Studia Math., 26 (1965), 11-–24 | DOI | MR | Zbl

[24] S. Parameswaran, “Partition functions whose logarithms are slowly oscillating”, Trans. Amer. Math. Soc., 100 (1961), 217-–240 | DOI | MR | Zbl

[25] E. Seneta, Regularly Varying Functions, Springer-Verlag, Berlin, 1976 | MR | Zbl

[26] U. Stadtmüller, R. Trautner, “Tauberian theorems for Laplace transforms”, J. Reine Angew. Math., 311/312 (1979), 283-–290 | MR | Zbl

[27] A. L. Yakymiv, “Asymptotics properties of the state change points in a random record process”, Theory Probab. Appl., 31 (1987), 508-–512 | DOI | MR | Zbl

[28] A. L. Yakymiv, “Asymptotics of the probability of nonextinction of critical Bellman–Harris branching processes”, Proc. Steklov Inst. Math., 4, 1988, 189-–217