@article{AFST_1996_6_5_3_521_0,
author = {Anthony G. Pakes},
title = {A hitting time for {L\'evy} processes, with application to dams and branching processes},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {521--544},
year = {1996},
publisher = {Universit\'e Paul Sabatier},
address = {Toulouse},
volume = {Ser. 6, 5},
number = {3},
doi = {10.5802/afst.838},
mrnumber = {1440948},
zbl = {0879.60074},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.838/}
}
TY - JOUR AU - Anthony G. Pakes TI - A hitting time for Lévy processes, with application to dams and branching processes JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 1996 SP - 521 EP - 544 VL - 5 IS - 3 PB - Université Paul Sabatier PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.838/ DO - 10.5802/afst.838 LA - en ID - AFST_1996_6_5_3_521_0 ER -
%0 Journal Article %A Anthony G. Pakes %T A hitting time for Lévy processes, with application to dams and branching processes %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 1996 %P 521-544 %V 5 %N 3 %I Université Paul Sabatier %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.838/ %R 10.5802/afst.838 %G en %F AFST_1996_6_5_3_521_0
Anthony G. Pakes. A hitting time for Lévy processes, with application to dams and branching processes. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 5 (1996) no. 3, pp. 521-544. doi: 10.5802/afst.838
[1] ) .- Fluctuation theory in continuous time, Adv. Appl. Prob. 7 (1975), pp. 705-766. | Zbl | MR
[2] ) .- Continuous branching processes and spectral positivity, Stoch. Processes Appl. 4 (1976), pp. 217-242. | Zbl | MR
[3] ) .- The work of Lajos Takács on probability theory. J. Appl. Prob. 31A (1994), pp. 29-39. | Zbl | MR
[4] ), ) and ) .- Regular Variation, C.U.P., Cambridge (1987). | Zbl | MR
[5] ) . - Generalized Gamma Convolutions and Related Classes of Distributions and Densities, Lecture Notes in Statistics, Springer-Verlag, New York, 76 (1992). | Zbl | MR
[6] ) .- On the first passage time for one class of processes with independent increments, Theor. Prob. Appl. 10 (1965), pp. 331-334. | Zbl | MR
[7] ) .- Stochastic Processes in Queueing Theory, Springer-Verlag, New York (1976). | Zbl | MR
[8] ) and ) .- Some interesting properties of Lagrangian distributions, Comm. Statist. 2 (1973), pp. 263-272. | Zbl | MR
[9] ) .- A note on Linnik's distribution, Statist. Prob. Lett. 9 (1990), pp. 305-306. | Zbl | MR
[10] ) .- The branching process method in Lagrange random variate generation, Comm. Statist. Simula. 21 (1992), pp. 1-14. | Zbl
[11] ) . - Probability Theory and its Applications, Wiley, New York, 2nd ed., 2 (1971).
[12] ) .- Sample functions of stochastic processes with stationary, independent increments, In: P. E. Ney and S. Port eds, Advances in Probability, Dekker, New York, 5 (1974), pp. 241-396. | Zbl | MR
[13] ) and ) .- A storage model with continuous infinitely divisible inputs, Proc. Camb. Phil. Soc. 59 (1963), pp. 417-429. | Zbl | MR
[14] ) and ) .- The Theory of Stochastic Processes II, Springer-Verlag, Berlin (1975). | Zbl | MR
[15] ) .- The supremum distribution of a Lévy process with no negative jumps, Adv. Appl. Prob. 9 (1977), pp. 417-422. | Zbl | MR
[16] ) .- On the distribution of the time to first emptiness of a store with stochastic input, J. Aust. Math. Soc. 4 (1964), pp. 506-517. | Zbl | MR
[17] ) . - Survival models for heterogeneous populations derived from stable distributions, Biometrika 73 (1986), pp. 387-396. | Zbl | MR
[18] ) and ) .- Independent and Stationary Sequences of Random Variables, Wolters-Noordhoff, Groningen (1971). | Zbl | MR
[19] ), ) and ) .- Univariate Discrete Distributions, Wiley, New York, 2nd ed. (1993). | Zbl | MR
[20] ) .- Branching Processes with Continuous State Space, Math. Centrum, Amsterdam (1979). | Zbl | MR
[21] ) . - The first passage time density for homogeneous skipfree walks on the continuum, Ann. Math. Statist. 34 (1963), pp. 1003-1011. | Zbl | MR
[22] ) .- Some problems in the theory of dams, J. Roy. Statist. Soc. Ser. B. 19 (1957), pp. 207-212. | Zbl | MR
[23] ) .- On continuous time models in the theory of dams, J. Aust. Math. Soc. 3 (1963), pp. 480-487. | Zbl | MR
[24] ) and ) .- Natural real exponential families with cubic variance functions, Ann. Statist. 18 (1990), pp. 1-37. | Zbl | MR
[25] ) .- An Introduction to Probability Theory, Clarendon Press, Oxford (1968). | Zbl | MR
[26] ) .- The multiplicative process, Ann. Math. Statist. 20 (1949), pp. 206-224. | Zbl | MR
[27] ) .- Some limit theorems for continuous-state branching processes, J. Aust. Math. Soc. Ser. A. 44 (1988), pp. 71-87. | Zbl | MR
[28] ) and ) .- Lagrange distributions and their limit theorems, SIAM J. Appl. Math. 32 (1977), pp. 745-754. | Zbl | MR
[29] ) .- Stochastic Storage Processes, Springer-Verlag, New York (1980). | Zbl | MR
[30] ) and ) .- On a regenerative phenomenon occurring in a storage model, J. Roy. Statist. Soc. Ser. B. 32 (1970), pp. 354-361. | Zbl | MR
[31] ) . - The two-sided exit problem for spectrally positive Lévy processes, Adv. Appl. Prob. 22 (1990), pp. 486-487. | Zbl | MR
[32] ) .- On a class of infinitely divisible processes represented as mixtures of Gaussian processes, In: S. Cambanis, G. Samarodnitsky et M. Taqqu, eds, Stable Processes and Related Topics, Birkäuser, Boston (1991), pp. 27-41. | Zbl | MR
[33] ) .- Inverse-Gaussian Distributions: A Case Study in Natural Exponential Families, Clarendon Press, Oxford (1993). | MR
[34] ) .- On local properties of processes with independent increments, Theor. Prob. Appl. 10 (1965), pp. 317-322. | Zbl
[35] ) .- Random Processes with Independent Increments, Kluwer Academic Publishers, Dordrecht (1991). | Zbl | MR
[36] ) .- Ratio limit theorems for random walks on groups, Trans. Amer. Math. Soc. 125 (1966), pp. 86-100. | Zbl | MR
[37] ) . - The distribution of the content of a dam when the input process has stationary independent increments, J. Math. Mech. 15 (1966), pp. 101-112. | Zbl | MR
[38] ) .- Combinatorial Methods in the Theory of Stochastic Processes, Wiley, New York (1967). | Zbl | MR
[39] ) .- Left-continuous random walk and the Lagrange expansion, Amer. Math. Monthly 82 (1975), pp. 494-499. | Zbl | MR
[40] ) .- A duality law in the class of infinitely divisible laws. English translation in Sel, Trans. Math. Statist. Prob. 5 (1961), pp. 201-209. | MR
[41] ) .- The first passage time of a level and the behavior at infinity for a class of processes with independent increments, Theor. Prob. Appl. 9 (1964), pp. 653-661. | Zbl | MR
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