Laws of large numbers for functions of random walks with positive drift
Compositio Mathematica, Volume 19 (1968) no. 4, p. 299-333
@article{CM_1968__19_4_299_0,
     author = {Stam, A. J.},
     title = {Laws of large numbers for functions of random walks with positive drift},
     journal = {Compositio Mathematica},
     publisher = {Wolters-Noordhoff Publishing},
     volume = {19},
     number = {4},
     year = {1968},
     pages = {299-333},
     zbl = {0239.60029},
     mrnumber = {243627},
     language = {en},
     url = {http://www.numdam.org/item/CM_1968__19_4_299_0}
}
Stam, A. J. Laws of large numbers for functions of random walks with positive drift. Compositio Mathematica, Volume 19 (1968) no. 4, pp. 299-333. http://www.numdam.org/item/CM_1968__19_4_299_0/

H.D. Brunk [1] On the Application of the Individual Ergodic Theorem to Discrete Stochastic Processes. Trans. Amer. Math. Soc. 78 (1955), 482-491. | Zbl 0068.12301

R.V. Chacon and D.S. Ornstein [2] A General Ergodic Theorem. Illinois J. of Math. 4 (1960), 153 -160. | Zbl 0134.12102

K.L. Chung and C. Derman [3] Non-recurrent Random Walks. Pacific J. of Math. 6 (1956), 441-447. | MR 81587 | Zbl 0072.35301

L.W. Cohen [4] On the Mean Ergodic Theorem. Ann. Math. 41 (1940), 505 - 509. | JFM 66.0560.02 | Zbl 0024.21401

C. Derman [5] A note on Nonrecurrent Random Walks. Proc. Amer. Math. Soc. 7 (1956), 762-765. | MR 83221 | Zbl 0072.35302

J.L. Doob [6] Stochastic Processes. Wiley, 1953. | MR 58896 | Zbl 0053.26802

N. Dunford and D.S. Miller [7] On the ergodic theorem, Trans. Amer. Math. Soc. 60 (1946), 538 - 549. | Zbl 0063.01187

W. Feller [8] An Introduction to Probability Theory and its Applications, Volume II. Wiley, 1966. | MR 210154 | Zbl 0039.13201

W. Feller and S. Orey [9] A Renewal Theorem. J. of Math. and Mech. 10 (1961), 619-624. | Zbl 0096.33401

T.E. Harris and H. Robbins [10] Ergodic Theory of Markov Chains Admitting an Infinite Invariant Measure. Proc. Nat. Ac. of Sc. U.S.A. 39 (1953), 860-864. | MR 56873 | Zbl 0051.10503

G. Kallianpur and H. Robbins [11] The Sequence of Sums of Independent Random Variables. Duke Math. J. 21 (1954), 285-307. | Zbl 0055.36704

M. Loève [12] Probability Theory, Sec. Ed., Van Nostrand, 1960. | MR 123342 | Zbl 0095.12201

E. Lukacs [13] Characteristic Functions. Griffin, 1960. | MR 124075 | Zbl 0087.33605

H. Robbins [14] On the Equidistribution of Sums of Independent Random Variables. Proc. Amer. Math. Soc. 4 (1953), 786-799. | MR 56869 | Zbl 0053.26704

M.G. Shur [15] On the Law of Large Numbers for Markov Processes. Theory of Prob. and its Appl. VIII (1963), 208-212. | Zbl 0127.35501

A.V. Skorokhod and N.P. Slobodenyuk [16] Limit Theorems for Random Walks I. Theory of Prob. and its Appl. X (1965), 596-606; II, id. XI (1966), 46-57. | MR 196794 | Zbl 0202.47403

F. Spitzer [17] Principles of Random Walk. Van Nostrand, 1964. | MR 171290 | Zbl 0119.34304

A.J. Stam [18] On Shifting Iterated Convolutions I. Compos. Math. 17 (1967), 268-280. | Numdam | MR 207019 | Zbl 0214.43704

L. Takács [19] Introduction to the Theory of Queues. Oxford Univ. Press, N.Y., 1962. | MR 133880 | Zbl 0106.33502