Geodesic
The matrix analogue of the Blackwell renewal theorem on the real line
Sbornik. Mathematics, Tome 197 (2006) no. 3, pp. 369-386 Cet article a éte moissonné depuis la source Math-Net.Ru

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The full analogue of Blackwell's theorem is proved for a matrix renewal measure on the whole real line, both in the non-lattice and in the lattice cases. A complete result on a decomposition of Stone type for a matrix renewal measure is obtained. Asymptotic properties of solutions of systems of integral equations of renewal type on the real line are established. Bibliography: 21 titles. 
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M. S. Sgibnev. The matrix analogue of the Blackwell renewal theorem on the real line. Sbornik. Mathematics, Tome 197 (2006) no. 3, pp. 369-386. http://geodesic.mathdoc.fr/item/SM_2006_197_3_a3/

[1] D. Blackwell, “Extension of a renewal theorem”, Pacific J. Math., 3 (1953), 315–320 | MR | Zbl

[2] V. Feller, Vvedenie v teoriyu veroyatnostei i ee prilozheniya, t. 2, Nauka, M., 1967

[3] C. Stone, “On absolutely continuous components and renewal theory”, Ann. Math. Stat., 37 (1966), 271–275 | DOI | MR | Zbl

[4] E. Arjas, E. Nummelin, R. L. Tweedie, “Uniform limit theorems for non-singular renewal and Markov renewal processes”, J. Appl. Probab., 15 (1978), 112–125 | DOI | MR | Zbl

[5] G. Alsmeyer, Erneuerungstheorie, B. G. Teubner, Stuttgart, 1991 | MR | Zbl

[6] K. S. Crump, “On systems of renewal equations”, J. Math. Anal. Appl., 30 (1970), 425–434 | DOI | MR | Zbl

[7] K. S. Crump, “On systems of renewal equations: the reducible case”, J. Math. Anal. Appl., 31 (1970), 517–528 | DOI | MR | Zbl

[8] T. A. Ryan, Jr., “A multidimensional renewal theorem”, Ann. Probab., 4 (1976), 656–661 | DOI | MR | Zbl

[9] N. B. Engibaryan, “Teoremy vosstanovleniya dlya sistemy integralnykh uravnenii”, Matem. sb., 189:12 (1998), 59–72 | MR | Zbl

[10] M. S. Sgibnev, “Razlozhenie Stouna dlya matrichnoi mery vosstanovleniya na poluosi”, Matem. sb., 192:7 (2001), 97–106 | MR | Zbl

[11] N. B. Engibaryan, “Konservativnye sistemy integralnykh uravnenii svertki na polupryamoi i vsei pryamoi”, Matem. sb., 193:6 (2002), 61–82 | MR | Zbl

[12] B. de Saporta, “Renewal theorem for a system of renewal equations”, Ann. Inst. H. Poincaré Probab. Statist., 39:5 (2003), 823–838 | DOI | MR | Zbl

[13] M. S. Sgibnev, “Systems of renewal equations on the line”, J. Math. Sci. Univ. Tokyo, 2003, 495–517 | MR | Zbl

[14] M. S. Sgibnev, “Sistemy integralnykh uravnenii tipa vosstanovleniya na pryamoi”, Differentsialnye uravneniya, 40:1 (2004), 128–137 | MR | Zbl

[15] R. Khorn, Ch. Dzhonson, Matrichnyi analiz, Mir, M., 1989 | MR

[16] E. Lukach, Kharakteristicheskie funktsii, Nauka, M., 1979 | MR | Zbl

[17] M. Loev, Teoriya veroyatnostei, IL, M., 1962

[18] B. L. Van der Varden, Algebra, Nauka, M., 1976 | MR

[19] E. L. Presman, “Metody faktorizatsii i granichnaya zadacha dlya summ sluchainykh velichin, zadannykh na tsepi Markova”, Izv. AN SSSR. Ser. matem., 33:4 (1969), 861–900 | MR | Zbl

[20] S. Asmussen, “Aspects of matrix Wiener–Hopf factorisation in applied probability”, Math. Sci., 14:2 (1989), 101–116 | MR | Zbl

[21] F. R. Gantmakher, Teoriya matrits, Nauka, M., 1967 | MR