TY - JOUR
T1 - Matrix geometric approach for random walks
T2 - stability condition and equilibrium distribution
AU - Kapodistria, S.
AU - Palmowski, Z.B.
PY - 2017/10/2
Y1 - 2017/10/2
N2 - In this paper, we analyze a sub-class of two-dimensional homogeneous nearest neighbor (simple) random walk restricted on the lattice using the matrix geometric approach. In particular, we first present an alternative approach for the calculation of the stability condition, extending the result of Neuts drift conditions
[
30
] and connecting it with the result of Fayolle et al. which is based on Lyapunov functions.
[
13
] Furthermore, we consider the sub-class of random walks with equilibrium distributions given as series of product forms and, for this class of random walks, we calculate the eigenvalues and the corresponding eigenvectors of the infinite matrix R appearing in the matrix geometric approach. This result is obtained by connecting and extending three existing approaches available for such an analysis: the matrix geometric approach, the compensation approach and the boundary value problem method. In this paper, we also present the spectral properties of the infinite matrix R.
AB - In this paper, we analyze a sub-class of two-dimensional homogeneous nearest neighbor (simple) random walk restricted on the lattice using the matrix geometric approach. In particular, we first present an alternative approach for the calculation of the stability condition, extending the result of Neuts drift conditions
[
30
] and connecting it with the result of Fayolle et al. which is based on Lyapunov functions.
[
13
] Furthermore, we consider the sub-class of random walks with equilibrium distributions given as series of product forms and, for this class of random walks, we calculate the eigenvalues and the corresponding eigenvectors of the infinite matrix R appearing in the matrix geometric approach. This result is obtained by connecting and extending three existing approaches available for such an analysis: the matrix geometric approach, the compensation approach and the boundary value problem method. In this paper, we also present the spectral properties of the infinite matrix R.
KW - math.PR
KW - Boundary value problem method
KW - compensation approach
KW - equilibrium distribution
KW - matrix geometric approach
KW - random walks
KW - spectrum
KW - stability condition
UR - http://www.scopus.com/inward/record.url?scp=85028749003&partnerID=8YFLogxK
U2 - 10.1080/15326349.2017.1359096
DO - 10.1080/15326349.2017.1359096
M3 - Article
VL - 33
SP - 572
EP - 597
JO - Stochastic Models
JF - Stochastic Models
SN - 1532-6349
IS - 4
ER -