Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
Given a probability space (Ω, A, P) and a complete separable metric space X, we consider R continuous and bounded solutions φ: X → R of the equations φ (x) = ∫Ω φ(ƒ(x, ω)) P(dω) and φ(x) = 1 - ∫Ωφ(ƒ(x, ω)) P(dω), assuming that the given function ƒ : X x Ω → X is controlled by a random variable L: Ω → (0, ∞) with -∞ < ∫Ω log L (ω) P (dω) < 0. An application to a refinement type equation is also presented.
Czasopismo
Rocznik
Tom
Strony
147--155
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
autor
- Silesian University Institute of Mathematics Bankowa 14, 40-007 Katowice, Poland, rkapica@math.us.edu.pl
Bibliografia
- [1] K. Baron, Recent results in the theory of functional equations in a single variable, Sem. LV, http://www.mathematik.uni-karlsruhe.de/˜semlv, No. 15 (2003), 16 pp.
- [2] K. Baron, W. Jarczyk, Recent results on functional equations in a single variable, perspectives and open problems, Aequationes Math. 61 (2001), 1–48.
- [3] K. Baron, W. Jarczyk, Random-valued functions and iterative functional equations, Aequationes Math. 67 (2004), 140–153.
- [4] K. Baron, M. Kuczma, Iteration of random-valued functions on the unit interval, Colloq. Math. 37 (1977), 263–269.
- [5] D. Dahmen, C.A. Micchelli, Continuous refinement equations and subdivision, Adv. Comput. Math. 1 (1993), 1–37.
- [6] I. Daubechies, Orthonormal bases of wavelets with compact support, Comm. Pure Appl. Math. 41 (1988), 909–996.
- [7] G. Derfel, A probabilistic method for studying a class of functional-differential equations [in Russian], Ukrain. Mat. Zh. 41 (1989), 1322–1327; English transl.: Ukrainian Math. J. 41 (1989), 1137–1141.
- [8] G. Derfel, N. Dyn, D. Levin, Generalized refinement equations and subdivision processes, J. Aprox. Theory 80 (1995), 272–297.
- [9] P. Diaconis, D. Freedman, Iterated random functions, SIAM Rev. 41 (1999), 45–76.
- [10] Ph. Diamond, A stochastic functional equation, Aequationes Math. 15 (1977), 225–23.
- [11] A.K. Grincevicjus, On the continuity of the distribution of a sum of dependent variables connected with independent walks on lines [in Russian], Teor. Verojatnost. i Primenen 19 (1974), 163–168; English translation: Teor. Probability Appl. 19 (1974), 163–168.
- [12] C.J. Himmelberg, Measurable relations, Fund. Math. 87 (1975), 53–72.
- [13] W. Jarczyk, Convexity properties of nonnegative solutions of a convolution equation, Selected topics in functional equations and iteration theory, Grazer Math. Ber. 316 (1992), 71–92.
- [14] R. Kapica, Sequences of iterates of random-valued vector functions and continuous solutions of a linear functional equation of infinite order, Bull. Polish Acad. Sci. Math. 50 (2002), 447–455.
- [15] R. Kapica, J. Morawiec, On a refinement type equation, J. Appl. Anal. 14 (2008), 251–257.
- [16] L.L. Schumaker, Spline functions: Basic theory, John Wiley, New York, 1981.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0001-0007