Skip to main content
SpringerLink
Log in

Random Motion on Simple Graphs

  • Published:
Methodology and Computing in Applied Probability Aims and scope Submit manuscript

Abstract

Consider a stochastic process that lives on n-semiaxes joined at the origin. On each ray it behaves as one dimensional Brownian Motion and at the origin it chooses a ray uniformly at random (Kirchhoff condition). The principal results are the computation of the exit probabilities and certain other probabilistic quantities regarding exit and occupation times.

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

Access this article

Log in via an institution

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

  • Barlow MT, Pitman JW, Yor M (1989) On Walsh’s Brownian motions. Sem. prob. XXIII. In: Lecture notes in mathematics, vol 1372. Springer, Berlin, pp 275–293

    Google Scholar 

  • Chung KL, Zambrini JC (2001) Introduction to random time and quantum randomness. In: Monographs of the Portuguese mathematical society. McGraw-Hill, Lisboa

    Google Scholar 

  • Deng D, Li Q (2009) Communication in naturally mobile sensor networks. Wireless algorithms, systems, and applications. Lect Notes Comput Sci 5682:295–304

    Article  Google Scholar 

  • Freidlin MI (1885) Functional integration and partial differential equations. Princeton University Press, Princeton

    Google Scholar 

  • Freidlin MI, Wentzell AD (1993) Diffusion processes on graphs and the averaging principle. Ann Probab 21(4):2215–2245

    Article  MathSciNet  MATH  Google Scholar 

  • Hristopulos DT (2003) Permissibility of fractal exponents and models of band-limited two-point functions for fGn and fBm random fields. Stoch Environ Res Risk Assess 17:191–216

    Article  MATH  Google Scholar 

  • James CS, Bilezikjian KT, Chysikopoulos VC (2005) Contaminant transport in a fracture with spatially variable aperture in the presence of monodisperse and polydisperse colloids. Stoch Environ Res Risk Assess 19:266–279

    Article  MATH  Google Scholar 

  • Karatzas I, Shreve SE (1991) Brownian motion and stochastic calculus, 2nd edn. Graduate texts in mathematics, vol 113. Springer, New York

    Google Scholar 

  • Mtundu ND, Koch RW (1987) A stochastic differential equation approach to soil moisture. Stoch Hydrol Hydraul 1:101–116

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, 15780, Athens, Greece

    Vassilis G. Papanicolaou, Effie G. Papageorgiou & Dimitris C. Lepipas

Authors
  1. Vassilis G. Papanicolaou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Effie G. Papageorgiou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dimitris C. Lepipas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vassilis G. Papanicolaou.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Papanicolaou, V.G., Papageorgiou, E.G. & Lepipas, D.C. Random Motion on Simple Graphs. Methodol Comput Appl Probab 14, 285–297 (2012). https://doi.org/10.1007/s11009-010-9203-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11009-010-9203-x

Keywords

AMS 2000 Subject Classifications

Search

Navigation