Abstract
In chapter 4, the analysis was based on specific derivations (a closure property in some sense) rendered possible by the finiteness of the order of the group. Hereafter, we shall obtain the complete solution when the order of the group of the random walk is arbitrary, i.e. possibly infinite. The main idea consists in the reduction to a factorization problem on a curve in the complex plane. Generally one comes up first with integral equations and, in a second step, with explicit integral forms by means of Weierstrass functions.
The erratum of this chapter is available at http://dx.doi.org/10.1007/978-3-642-60001-2_11
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Fayolle, G., Iasnogorodski, R., Malyshev, V. (1999). Solution in the Case of an Arbitrary Group. In: Random Walks in the Quarter-Plane. Applications of Mathematics Stochastic Modelling and Applied Probability, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60001-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-60001-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64217-3
Online ISBN: 978-3-642-60001-2
eBook Packages: Springer Book Archive