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Räumlich homogene Irrfahrten im Gitter. I: Stationäre Irrfahrten. II: Instationäre Irrfahrten. (German) Zbl 0107.34903

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[1] Chung, K. L.: Markov chains with stationary transition probabilities. Berlin-Göttingen-Heidelberg: Springer-Verlag 1960. · Zbl 0092.34304
[2] Doob, J. L.: Stochastic processes. New York: J. Wiley & Sons, Inc. 1953. · Zbl 0053.26802
[3] Feller, W.: An introduction to probability theory and its applications. 2. Aufl. New York: J. Wiley & Sons, Inc. 1958
[4] Bellman, R., andR. Kalaba: Random walk, scattering and invariant imbedding. Proc. Nat. Acad. Sci. U. S.43, 930?933 (1957). · Zbl 0084.35603
[5] Bellman, R., andR. Kalaba: Invariant imbedding, random walk and scattering. II. Discrete versions. J. Math. Mech.9, 411?419 (1960). · Zbl 0093.14502
[6] Chandrasekhar, S.: Stochastic problems in physics and astronomy. Phys. Rev.36, 1?89 (1943). · Zbl 0061.46403
[7] Chung, K. L.: Contributions to the theory of Markov chains. J. Res. Nat., Bur. Stand.50, 203?208 (1953). · Zbl 0053.27201
[8] Chung, K. L.: Contributions to the theory of Markov chains. II.. Trans. Am. Math. Soc.76, 397?419 (1954). · Zbl 0058.34602
[9] Chung, K. L., andW. H. J. Fuchs: On the distribution of values of sums of random variables. Mem. Am. Math. Soc.6, 1?12 (1951). · Zbl 0042.37502
[10] Derman, C.: Some contributions to the theory of denumerable Markov chains. Trans. Am. Math. Soc.79, 541?555 (1955). · Zbl 0065.11405
[11] Domb, C.: On multiple returns in the random walk problem. Proc. Cambridge Phil. Soc.50, 586?591 (1954). · Zbl 0056.12602
[12] Eberl, W.: Ein Zufallsweg in einer Markoffschen Kette von Alternativen. Monatsh. Math.58, 137?142 (1954). · Zbl 0056.36201
[13] Feldheim, E.: Sur les probabilités en chaine. Math. Ann.112, 775?780 (1936). · JFM 62.0604.02
[14] Feller, W.: The integrodifferential equations of purely discontinuous Markov processes. Trans. Am. Math. Soc.48, 488?515 (1940). · JFM 66.0624.02
[15] Foster, F. G., andI. J. Good: On a generalisation of Pólyas random-walk theorem. Quart. J. Math., Oxford Ser. 2,4, 120?126 (1953). · Zbl 0050.13903
[16] Gillis, J.: Centrally biased discrete random walk. Quart. J. Math., Oxford Ser. 2,7, 144?152 (1956). · Zbl 0073.13301
[17] Henze, E.: Beiträge zum Irrfahrtproblem. Diss. TH Stuttgart 1958. · Zbl 0082.13201
[18] Henze, E.: Lösung einiger Probleme aus der Theorie der diskreten Irrfahrt. Z. Angew. Math. Mech.39, 371?373 (1959). · Zbl 0100.34202
[19] Henze, E.: Zur Theorie der diskreten unsymmetrischen Irrfahrt. Z. Angew. Math. Mech.41, 1?9 (1961). · Zbl 0109.10802
[20] Karlin, S., andJ. McGregor: Random walks. Illinois J. Math.3, 66?81 (1959). · Zbl 0104.11804
[21] Klein, G.: Generalisation of the classical random-walk problem, and a simple model of Brownian motion based thereon. Proc. Roy. Soc. Edinburgh, Sect. A,63, 268?279 (1952). · Zbl 0049.26204
[22] Kolmogoroff, A.: Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung. Math. Ann.104, 413?458 (1931). · Zbl 0001.14902
[23] Lehman, R. S., andG. H. Weiss: A study of the restricted random walk. J. Soc. Ind. Appl. Math.6, 257?278 (1958). · Zbl 0090.34902
[24] McCrea, W. H., andF. J. W. Whipple: Random paths in two and three dimensions. Proc. Roy. Soc. Edinburgh LX (1939/40), 281?298. · Zbl 0027.33903
[25] Mercer, A., andC. S. Smith: A random walk in which the steps occur randomly in time. Biometrica46, 30?35 (1959). · Zbl 0088.35002
[26] Montroll, E. W.: On the theory of Markov chains. Ann. Math. Statistics18, 18?36 (1947). · Zbl 0032.17203
[27] Pólya, G.: Über eine Aufgabe der Wahrscheinlichkeitsrechnung betreffend die Irrfahrt im Straßennetz. Math. Ann.84, 149?160 (1921). · JFM 48.0603.01
[28] Sack, R. A.: Restricted random walks and the use of moments. Phil. Mag. (8),3, 504?507 (1958). · Zbl 0082.13202
[29] Sjöberg, B.: Über lineare Irrfahrt mit Absorptionsschranken. Acta Acad. Abo21, Nr. 13 (1958). · Zbl 0098.32404
[30] Stöhr, A.: Über einige lineare partielle Differenzengleichungen mit konstanten Koeffizienten. I., II., III. Math. Nachr.3, 208?242, 295?315, 330?357 (1950). · Zbl 0038.24103
[31] Watanabe, Y.: Aufgaben betreffend das Irrfahrtproblem. J. Gakugei, Tokushima Univ.6, 41?49 (1955). · Zbl 0066.11405
[32] Watanabe, Y.: Einige Erweiterung des Pólyaschen Irrfahrtproblems. J. Gakugei, Tokushima Univ.8, 13?25 (1957). · Zbl 0080.35103
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