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

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

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

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

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

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

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

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

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

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. | Zbl | MR

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

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

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

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

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

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. | Zbl | MR

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

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

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