Long-term returns in stochastic
Teoriâ slučajnyh processov, Tome 13 (2007) no. 4, pp. 247-261.

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We consider the behavior of integral functional of the solution of stochastic differential equation with coefficients contained small parameter. The dependence on the order of small parameter in every term of equation with Wiener process and Poisson measure term is studied. We observe the convergence of the long-term return, using an extension of the Cox-Ingersoll-Ross stochastic model of the short interest rate. Obtained results are applied for studying of two-factor stochastic interest rate model.
Keywords: Stochastic differential equation, integral functional, long-term return, limit behavior, small parameter.
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Vladimir Zubchenko. Long-term returns in stochastic. Teoriâ slučajnyh processov, Tome 13 (2007) no. 4, pp. 247-261. http://geodesic.mathdoc.fr/item/THSP_2007_13_4_a18/

[1] Salminen, P., Yor, M., “Properties of perpetual integral functionals of Brownian motion with drift”, Ann. I.H.P., 41 (3) (2005), 335–347

[2] Khoshnevisan, D., Salminen, P., Yor, M., “A note on a.s. finiteness of perpetual integral functionals of diffusions”, Elect. Comm. in Probab., 11 (2006), 108–117

[3] Borysenko O., Malyshev I., “The limit behaviour of integral functional of the solution of stochastic di?erential equation depending on small parameter”, Theory of Stochastic Processes, 7 (23):1–2 (2001), 30–36

[4] Cox, J. C., Ingersoll, J. E., Ross, S. A., “A theory of the term structure of interest rate”, Econometrica, 53 (1985), 385–407

[5] Deelstra, G., Delbaen, F., “Long-term returns in stochastic interest rate models”, Insurance: Mathematics and Economics, 17 (1995), 163–169

[6] Skorokhod, A. V., Elements of the Probability Theory and the Theory of Random Processes, Vysha Shkola, Kiev, 1980

[7] Skorokhod, A. V., Studies in the Theory of Random Processes, Kiev Univ. publisher, 1961

[8] Gikhman, I. I., Skorokhod, A. V., The Theory of Stochastic Processes, v. I, Nauka, Moscow, 1971

[9] Korolyuk, V. S.,Portenko N. I.,Skorokhod, A. V., Turbin, A. F., Reference book on the Probability Theory and Mathematical Statistics, Naukova Dumka, Kiev, 1978

[10] Gikhman, I. I., Skorokhod, A. V., Stochastic Differential Equations and their Applications, Naukova Dumka, Kiev, 1982

[11] Deelstra, G., Delbaen, F., “Long-term returns in stochastic interest rate models: different convergence results”, Applied Stoch. Models and Data Analysis, 13 (1998), 401–407