Advertisement

Journal of Mathematical Sciences

, Volume 204, Issue 3, pp 271–279 | Cite as

Convolution equation with a kernel represented by gamma distributions

  • Ani G. Barseghyan
Article

Abstract

The convolution integral equation is considered on the half-line and on a finite interval. Its kernel function is the distribution density of a random variable represented as a two-sided mixture of gamma distributions. The method of numerical-analytical solution of this equation is developed, and the solution of the homogeneous conservative equation on the half-line is constructed.

Keywords

Convolution operator factorization gamma distribution numerical-analytical solution homogeneous conservative equation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. G. Arabadzhyan and N. B. Engibaryan, “Convolution equations and nonlinear functional equations,” in: Totals of Science and Technique, Math. Analysis [in Russian], VINITI, Moscow, 1984, 22, pp. 175–244.Google Scholar
  2. 2.
    A. G. Barseghyan, “Integral equation with summarily difference kernel on a finite interval,” Izv. NAN Respub. Armen. Mat., 40:3, 22–32 (2005).Google Scholar
  3. 3.
    A. A. Borovkov, Probability Theory [in Russian], URSS, Inst. of Math., SB RAS, Moscow–Novosibirsk, 1999.Google Scholar
  4. 4.
    N. B. Engibaryan and A. G. Barseghyan, “Random walks and mixtures of gamma-distributions,” Teor. Ver. Pril., 55, 571–577 (2010).CrossRefGoogle Scholar
  5. 5.
    I. Feldman, I. Gohberg, and N. Krupnik, “Convolution equations on finite intervals and factorization of matrix functions,” Integr. Equ. Oper. Theory, 36, 201–211 (2000).CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    W. Feller, An Introduction to Probability Theory and Its Applications, Wiley, New York, 1970.Google Scholar
  7. 7.
    J. H. B. Kemperman, “A Wiener–Hopf type method for a general random walk with a two-sided boundary,” Ann. Math. Statist., 34, No. 4, 1168–1193 (1963).CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    V. I. Lotov, “On random walks in a strip,” Teor. Ver. Pril., 36, 160–165 (1991).MATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute of Mathematics of the National Academy of Sciences of Republic of ArmeniaYerevanRepublic of Armenia

Personalised recommendations