Skip to main content
Springer Nature Link
Log in

Ruin problem for an inhomogeneous semicontinuous integer-valued process

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

For a process ξ(t = ξ1(t)+χ(t), t≥0, ξ(0) = 0, inhomogeneous with respect to time, we investigate the ruin problem associated with the corresponding random walk in a finite interval, (here, ξ1 (t) is a homogeneous Poisson process with positive integer-valued jumps and χ(t) is an inhomogeneous lower-semicontinuous process with integer-valued jumps ξ n ≥-1).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. S. Korolyuk, Boundary-Value Problems for Complex Poisson Processes [in Russian] Naukova Dumka, Kiev 1975.

    Google Scholar 

  2. V. S. Korolyuk, N. S. Bratiichuk, and B. Pirdzhanov, Boundary-Value Problems for Random Walks [in Russian] Ylym, Ashkhabad 1987.

    Google Scholar 

  3. N. S. Bratiichuk and D. V. Gusak, Boundary-Value Problems for Processes with Independent Increments [in Russian] Naukova Dumka, Kiev 1990.

    Google Scholar 

  4. D. V. Gusak, “On generalized semicontinuous integer-valued Poisson processes with reflection,” Teor. Ver. Mat. Statist., Issue 59, 37–43 (1998).

    Google Scholar 

  5. V. S. Korolyuk and B. Pirliev, “Random walk on a superposition of two renewal processes,” Ukr. Mat. Zh., 36, No. 4, 431–437 (1984).

    MathSciNet  Google Scholar 

  6. N. S. Bratiichuk and B. Pirliev, “On the value of a jump over a level by a random walk on a superposition of two renewal processes,” Ukr. Mat. Zh., 37, No. 5, 689–695 (1985).

    MathSciNet  Google Scholar 

  7. N. S. Bratiichuk and B. Pirdzhanov, “A limit theorem for the hitting time and the value of a jump over a level by a regenerating semi-Markovian walk,” in: Theory of Random Processes and Its Applications [in Russian], Naukova Dumka, Kiev (1990), pp. 41–48.

    Google Scholar 

  8. D. V. Gusak, Boundary-Value Problems for Processes with Independent Increments on Finite Markovian Chains and for Semi-Mar-kovian Processes [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1998).

    Google Scholar 

  9. D. V. Gusak and A. M. Rozumenko, “On extrema of integer-valued processes defined by sums of a random number of addenda,” Random Oper. Stochast. Equal., 3, No. 1, 87–100 (1995).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Authors
  1. D. V. Gusak
    View author publications

    You can also search for this author inPubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gusak, D.V. Ruin problem for an inhomogeneous semicontinuous integer-valued process. Ukr Math J 52, 234–248 (2000). https://doi.org/10.1007/BF02529636

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02529636

Keywords