[1] Berman S M. Sojourns and extremes of Gaussian processes. The Annals of Probability. 1974, 2(6): 999–1026 [2] Berman S M. Sojourns and extremes of stationary processes. The Annals of Probability. 1982, 10(1): 1–46 [3] Berman S M. Sojourns and Extremes of Stochastic Processes. Wadsworth & Brooks/Cole Statisitics/Probability Series, Pacific Grove, CA: Wadsworth & Brooks/Cole Advanced Books & Software, 1992 [4] Pickands III J. Maxima of stationary Gaussian processes. Z Wahrscheinlichkeitstheorie und Verw Gebiete, 1967, 7(2): 190–223 [5] Pickands III J. Asymptotic properties of the maximum in a stationary Gaussian process. Transactions of the American Mathematical Society, 1969, 145: 75–86 [6] Pickands III J. Upcrossing probabilities for stationary Gaussian processes. Transactions of the American Mathematical Society, 1969, 145: 51–73 [7] Piterbarg V I. On the paper by J. Pickands “Upcrossing probabilities for stationary Gaussian processes”. Vestnik Moskovskogo Universiteta Serija I. Matematika, Mehanika, 1972, 27(5): 25–30 [8] Piterbarg V I, Prisjažnjuk V P. Asymptotic behavior of the probability of a large excursion for a nonstationary Gaussian process. Theory of Probability & Mathematical Statistics, 1979, 18(2): 131–144 [9] Piterbarg V I. Asymptotic Methods in the Theory of Gaussian Processes and Fields. Translations of Mathematical Monographs 148. Providence, RI: American Mathematical Society, 1996 [10] Hüsler J, Piterbarg V I. Extremes of a certain class of Gaussian processes. Stochastic Processes and Their Applications, 1999, 83(2): 257–271 [11] Piterbarg V I. Large deviations of a storage process with fractional Brownian motion as input. Extremes, 2001, 4(2): 147–164 [12] Dȩbicki K, Hashorva E, Soja-Kukieła N. Extremes of homogeneous Gaussian random fields. Journal of Applied Probability, 2015, 52(1): 55–67 [13] Dȩbicki K, Hashorva E, Liu P. Extremes of γ-reflected Gaussian process with stationary increments. ESAIM Probability & Statistics, 2017, 21: 495–535 [14] Hashorva E, Ji L. Piterbarg theorems for chi-processes with trend. Extremes, 2015, 18(1): 37–64 [15] Dȩbicki K, Hashorva E, Ji L, Tabiś K. Extremes of vector-valued Gaussian processes: Exact asymptotics. Stochastic Processes and Their Applications, 2015, 125(11): 4039–4065 [16] Dȩbicki K, Engelke S, Hashorva E. Generalized Pickands constants and stationary max-stable processes. Extremes, 2017, 20: 493–517 [17] Dȩbicki K, Hashorva E, Liu P. Extremes of Gaussian random fields with regularly varying dependence structure. Extremes, 2017, 20: 333–393 [18] Dȩbicki K, Hashorva E. Approximation of supremum of max-stable stationary processes & Pickands constants. Journal of Theoretical Probability, 2020, 33: 444–464 [19] Dȩbicki K, Michna Z, Peng X F. Approximation of sojourn times of Gaussian processes. Methodology and Computing in Applied Probability, 2019, 21(4): 1183–1213 [20] Dȩbicki K, Hashorva E, Liu P. Uniform tail approximation of homogenous functionals of Gaussian fields. Advances in Applied Probability, 2017, 49(04): 1037–1066 [21] Berman S M. Sojourns and extremes of a diffusion process on a fixed interval. Advances in Applied Probability, 1982, 14(4): 811–832 [22] Berman S M. Sojourns of stationary processes in rare sets. The Annals of Probability. 1983, 11(4): 847–866 [23] Berman S M. A sojourn limit theorem for Gaussian processes with increasing variance. Stochastics, 2007, 13(4): 281–298 [24] Berman S M. Extreme sojourns for random walks and birth-and-death processes. Communications in Statistics. Stochastic Models, 1986, 2(3): 393–408 [25] Berman S M. Sojourns and extremes of a stochastic process defined as a random linear combination of arbitrary functions. Communications in Statistics. Stochastic Models 4, 1988, 49(1): 1–43 [26] Berman S M. Extreme sojourns of diffusion processes. Annals of Probability, 1988, 16(1): 361–374 [27] Berman S M. Sojourn times in a cone for a class of vector Gaussian processes. SIAM Journal on Applied Mathematics, 1989, 49(2): 608–616 [28] Berman S M. Sojourns of vector Gaussian processes inside and outside spheres. Probability Theory and Related Fields, 1984, 66(4): 529–542 [29] Bingham N H, Goldie C M, Teugels J L. Regular Variation. Cambridge: Cambridge University Press, 1987 [30] Fernique X. Regularité des trajectoires des fonctions aléatoires Gaussiennes (in French). Lecture Notes in Math, 1975, 480: 1–96 [31] Adler R J. An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes. Lecture Notes-Monograph Series, 12. Hayward, Californla: Institute of Mathematical Statistics, 1990 [32] Adler R J, Taylor J E. Random Fields and Geometry. New York: Springer, 2007 [33] Karatzas I, Shreve S E. Brownian Motion and Stochastic Calculus. 2nd ed. New York: Springer, 1998 [34] Cheng S H. The Fundementals of Measurement Theory and Probability Theory (in Chinese). Beijing: Peking University Press, 2004 [35] Li X P. Fundementals of Probability Theory (in Chinese). Beijing: Higher Education Press, 2010 [36] Dȩbicki K, Hashorva E, Ji L P. Parisian ruin over a finite-time horizon. Science China Mathematics, 2016, 59(3): 557–572 |