Uittreksel
| Taal | Engels |
|---|---|
| Pagina's | 572-597 |
| Tijdschrift | Stochastic Models |
| Volume | 33 |
| Nummer van het tijdschrift | 4 |
| DOI's | |
| Status | Gepubliceerd - 31 aug 2017 |
Vingerafdruk
Trefwoorden
- math.PR
Citeer dit
}
Matrix geometric approach for random walks : stability condition and equilibrium distribution. / Kapodistria, S. (Corresponding author); Palmowski, Z.B.
In: Stochastic Models, Vol. 33, Nr. 4, 31.08.2017, blz. 572-597.Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review
TY - JOUR
T1 - Matrix geometric approach for random walks
T2 - Stochastic Models
AU - Kapodistria,S.
AU - Palmowski,Z.B.
PY - 2017/8/31
Y1 - 2017/8/31
N2 - In this paper, we analyse a sub-class of two-dimensional homogeneous nearest neighbour (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 $\mathbf{R}$ 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 $\mathbf{R}$.
AB - In this paper, we analyse a sub-class of two-dimensional homogeneous nearest neighbour (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 $\mathbf{R}$ 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 $\mathbf{R}$.
KW - math.PR
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 -