Citation:
Ya. G. Sinai, “On the Distribution of the First Positive Sum for a Sequence of Independent Random Variables”, Teor. Veroyatnost. i Primenen., 2:1 (1957), 126–135; Theory Probab. Appl., 2:1 (1957), 122–129
\Bibitem{Sin57}
\by Ya.~G.~Sinai
\paper On the Distribution of the First Positive Sum for a Sequence of Independent Random Variables
\jour Teor. Veroyatnost. i Primenen.
\yr 1957
\vol 2
\issue 1
\pages 126--135
\mathnet{http://mi.mathnet.ru/tvp4964}
\transl
\jour Theory Probab. Appl.
\yr 1957
\vol 2
\issue 1
\pages 122--129
\crossref{https://doi.org/10.1137/1102009}
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V. A. Vatutin, C. Dong, E. E. Dyakonova, “Some functionals for random walks and critical branching processes in an extremely unfavourable random environment”, Sb. Math., 215:10 (2024), 1321–1350
V. A. Vatutin, C. Dong, E. E. Dyakonova, “Random walks conditioned to stay nonnegative and branching processes in an unfavourable environment”, Sb. Math., 214:11 (2023), 1501–1533
V. I. Lotov, “O svoistvakh granichnykh funktsionalov dlya sluchainogo bluzhdaniya s ustoichivymi raspredeleniyami skachkov”, Sib. elektron. matem. izv., 20:1 (2023), 455–464
Hui He, Jingning Liu, Mei Zhang, “On Seneta–Heyde scaling for a stable branching random walk”, Adv. Appl. Probab., 50:2 (2018), 565
Francesco Caravenna, Loïc Chaumont, “An invariance principle for random walk bridges conditioned to stay positive”, Electron. J. Probab., 18:none (2013)
Ya. G. Sinai, “Limit theorem for trigonometric sums. Theory of curlicues”, Russian Math. Surveys, 63:6 (2008), 1023–1029
N.H. Bingham, Handbook of Statistics, 19, Stochastic Processes: Theory and Methods, 2001, 171
S. P. Novikov, L. A. Bunimovich, A. M. Vershik, B. M. Gurevich, E. I. Dinaburg, G. A. Margulis, V. I. Oseledets, S. A. Pirogov, K. M. Khanin, N. N. Chentsova, “Yakov Grigor'evich Sinai (on his sixtieth birthday)”, Russian Math. Surveys, 51:4 (1996), 765–778
R. A. Doney, P. E. Greenwood, “On the joint distribution of ladder variables of random walk”, Probab. Th. Rel. Fields, 94:4 (1993), 457
P. Greenwood, E. Perkins, “Limit theorems for excursions from a moving boundary”, Theory Probab. Appl., 29:4 (1985), 731–743
P. Greenwood, E. Omey, J. L. Teugels, “Harmonic renewal measures”, Z. Wahrscheinlichkeitstheorie verw Gebiete, 59:3 (1982), 391
P. Greenwood, E. Omey, J. L. Teugels, “Harmonic renewal measures and bivariate domains of attraction in fluctuation theory”, Z. Wahrscheinlichkeitstheorie verw Gebiete, 61:4 (1982), 527
N. H. Bingham, “Maxima of sums of random variables and suprema of stable processes”, Z. Wahrscheinlichkeitstheorie verw Gebiete, 26:4 (1973), 273
B. A. Rogozin, “The distribution of the first hit for stable and asymptotically stable walks on an interval”, Theory Probab. Appl., 17:2 (1973), 332–338
B. A. Rogozin, “The distribution of the first ladder moment and height and fluctuations of random walk”, Theory Probab. Appl., 16:4 (1971), 575–595
N. U. Prabhu, “Limit theorems for the single server queue with traffic intensity one”, Journal of Applied Probability, 7:1 (1970), 227
N. U. Prabhu, “Limit theorems for the single server queue with traffic intensity one”, J. Appl. Probab., 7:01 (1970), 227
V. I. Rotar', “On moments of the time and the value of the first jump over a curvilinear bound”, Theory Probab. Appl., 12:4 (1967), 690–695
B. A. Rogozin, “On some classes of processes with independent increments”, Theory Probab. Appl., 10:3 (1965), 479–483