Download this PDF file Fullscreen Fullscreen Off
References
- F. Avram ; T. Chan ; M. Usabel . On the valuation of constant barrier options under spectrally one-sided exponential Lévy models and Carr's approximation for American puts. Stochastic Process. Appl. 100 (2002), 75--107. MR1919609 (2003d:91041)
- F. Avram ; A. E. Kyprianou ; M. R. Pistorius . Exit problems for spectrally negative Lévy processes and applications to (Canadized) Russian options. Ann. Appl. Probab. 14 (2004), no. 1, 215--238. MR2023021 (2005c:60053)
- F. Avram ; Z. Palmowski ; M. R. Pistorius . On the optimal dividend problem for a spectrally negative Lévy process. Ann. Appl. Probab. 17 (2007), no. 1, 156--180. MR2292583 (2008e:93121)
- R. Bekker ; O. Boxma ; O. Kella . Queues with delays in two state strategies and Lévy input. EURANDOM, report 2007-08 (2007). Math. Review number not available.
- C. Berg ; G. Forst . Potential theory on locally compact abelian groups. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 87. Springer-Verlag, New York-Heidelberg, 1975. vii+197 pp. MR0481057 (58 #1204)
- J. Bertoin . Lévy processes. Cambridge Tracts in Mathematics, 121. Cambridge University Press, Cambridge, 1996. x+265 pp. ISBN: 0-521-56243-0 MR1406564 (98e:60117)
- J. Bertoin . Exponential decay and ergodicity of completely asymmetric Lévy processes in a finite interval. Ann. Appl. Probab. 7 (1997), no. 1, 156--169. MR1428754 (98d:60147)
- J. Bertoin . Regenerative embedding of Markov sets. Probab. Theory Related Fields 108 (1997), no. 4, 559--571. MR1465642 (98h:60013)
- J. Bertoin ; B. Roynette ; M. Yor . Some connections between (sub)critical branching mechanisms and Bernstein functions. Preprint (2004). Math. Review number not available.
- N. H. Bingham . Continuous branching processes and spectral positivity. Stochastic Processes Appl. 4 (1976), no. 3, 217--242. MR0410961 (53 #14701)
- L. Bondesson . Generalized gamma convolutions and related classes of distributions and densities. Lecture Notes in Statistics, 76. Springer-Verlag, New York, 1992. viii+173 pp. ISBN: 0-387-97866-6 MR1224674 (94g:60031)
- L. Chaumont Sur certains processus de Lévy conditionnés à rester positifs. (French) [On certain Levy processes that are conditioned to stay positive] Stochastics Stochastics Rep. 47 (1994), no. 1-2, 1--20. MR1787140 (2001e:60093)
- L. Chaumont Conditionings and path decompositions for Lévy processes. Stochastic Process. Appl. 64 (1996), no. 1, 39--54. MR1419491 (98b:60131)
- L. Chaumont ; A. E. Kyprianou ; J. C. Pardo. Some explicit identities associated with positive self-similar Markov processes. Preprint (2007). Math. Review number not available.
- S. N. Chiu ; C. Yin . Passage times for a spectrally negative Lévy process with applications to risk theory. Bernoulli 11 (2005), no. 3, 511--522. MR2146892 (2006g:60074)
- C. Donati-Martin ; M. Yor . Further examples of explicit Krein representations of certain subordinators. Publ. Res. Inst. Math. Sci. 43 (2007), no. 2, 315--328. MR2341013 (2008f:60050)
- R. A. Doney . Hitting probabilities for spectrally positive Lévy processes. J. London Math. Soc. (2) 44 (1991), no. 3, 566--576. MR1149016 (93b:60166)
- R. A. Doney . Some excursion calculations for spectrally one-sided Lévy processes. Séminaire de Probabilités XXXVIII, 5--15, Lecture Notes in Math., 1857, Springer, Berlin, 2005. MR2126963 (2006b:60098)
- R. A. Doney . Fluctuation theory for Lévy processes. Lectures from the 35th Summer School on Probability Theory held in Saint-Flour, July 6--23, 2005. Edited and with a foreword by Jean Picard. Lecture Notes in Mathematics, 1897. Springer, Berlin, 2007. x+147 pp. ISBN: 978-3-540-48510-0; 3-540-48510-4 MR2320889
- R. A. Doney ; A. E. Kyprianou . Overshoots and undershoots of Lévy processes. Ann. Appl. Probab. 16 (2006), no. 1, 91--106. MR2209337 (2007b:60117)
- P. Dube ; F. Guillemin ; R. R. Mazumdar . Scale functions of Lévy processes and busy periods of finite-capacity $M/GI/1$ queues. J. Appl. Probab. 41 (2004), no. 4, 1145--1156. MR2122808 (2005m:60208)
- D. J. Emery . Exit problem for a spectrally positive process. Advances in Appl. Probability 5 (1973), 498--520. MR0341623 (49 #6370)
- H. Furrer . Risk processes perturbed by $alpha$-stable Lévy motion. Scand. Actuar. J. (1998) no. 1, 59--74. MR1626676 (99e:60198)
- J. Hawkes . On the potential theory of subordinators. Z. Warscheinlichkeitstheorie und Verw. Gebiete 33 (1975/76), no. 2, 113--132. MR0388553 (52 #9389)
- J. Hawkes . Intersections of Markov random sets. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 37 (1976/77), no. 3, 243--251. MR0483035 (58 #3064)
- B. Hilberink ; L. C. G. Rogers . Optimal capital structure and endogenous default. Finance Stoch. 6 (2002), no. 2, 237--263. MR1897961
- F. Hirsch . Familles d'opérateurs potentiels. (French) Collection of articles dedicated to Marcel Brelot on the occasion of his 70th birthday. Ann. Inst. Fourier (Grenoble) 25 (1975), no. 3-4, xxii, 263--288. MR0402088 (53 #5911)
- F. Hubalek ; A. E. Kyprianou . Old and new examples of scale functions for spectrally negative Lévy processes. Preprint (2007). Math. Review number not available.
- T. Huillet . Energy cascades as branching processes with emphasis on Neveu's approach to Derrida's random energy model. Adv. in Appl. Probab. 35 (2003), no. 2, 477--503. MR1970484 (2005k:60236)
- N. Jacob Pseudo differential operators and Markov processes. Vol. I. Fourier analysis and semigroups. Imperial College Press, London, 2001. xxii+493 pp. ISBN: 1-86094-293-8 MR1873235 (2003a:47104)
- L. F. James ; B. Roynette ; M. Yor . Generalized gamma convolutions, Dirichlet means, Thorin measures, with explicit examples. Preprint (2007). Math. Review number not available.
- J. F. C. Kingman . Markov transition probabilities. I. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 7 (1967) 248--270. MR0217886 (36 #975)
- C. Klüppelberg ; A. E. Kyprianou . On extreme ruinous behaviour of Lévy insurance risk processes. J. Appl. Probab. 43 (2006), no. 2, 594--598. MR2248586 (2007k:91169)
- C. Klüppelberg ; A. E. Kyprianou ; R. A. Maller . Ruin probabilities and overshoots for general Lévy insurance risk processes. Ann. Appl. Probab. 14 (2004), no. 4, 1766--1801. MR2099651 (2005j:60097)
- V. S. Koroljuk . Boundary problems for a compound Poisson process. (Russian) Teor. Verojatnost. i Primenen. 19 (1974), 3--14. MR0336824 (49 #1597)
- V. S.Koroljuk . Ruin problems for a compound Poisson process. (Russian) Teor. Verojatnost. i Primenen. 20 (1975), no. 2, 382--384. MR0402940 (53 #6754)
- N. Krell . Multifractal spectra and precise rates of decay in homogeneous fragmentations. Stochastic Process. Appl. 118 (2008), no. 6, 897--916. MR2418249
- A. E. Kyprianou . Introductory lectures on fluctuations of Lévy processes with applications. Universitext. Springer-Verlag, Berlin, 2006. xiv+373 pp. ISBN: 978-3-540-31342-7; 3-540-31342-7 MR2250061 (2008a:60003)
- A. E. Kyprianou ; Z. Palmowski . Quasi-stationary distributions for Lévy processes. Bernoulli 12 (2006), no. 4, 571--581. MR2248228 (2007k:60136)
- A. E. Kyprianou ; Z. Palmowski . Distributional study of de Finetti's dividend problem for a general Lévy insurance risk process. J. Appl. Probab. 44 (2007), no. 2, 428--443. MR2340209
- A. E. Kyprianou ; B. A. Surya . Principles of smooth and continuous fit in the determination of endogenous bankruptcy levels. Finance Stoch. 11 (2007), no. 1, 131--152. MR2284015 (2008b:91069)
- A. Lambert . Completely asymmetric Lévy processes confined in a finite interval. Ann. Inst. H. Poincaré Probab. Statist. 36 (2000), no. 2, 251--274. MR1751660 (2001f:60049)
- A. Lambert . Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct. Electron. J. Probab. 12 (2007), no. 14, 420--446 (electronic). MR2299923 (2008b:60183)
- R. Loeffen . On optimality of the barrier strategy in De Finetti's dividend problem for spectrally negative Lévy processes. To appear in Ann. Appl. Probab. (2008). Math. Review number not available.
- P. Patie .Law of the exponential functional of a new family of one-sided Lévy processes via self-similar continuous state branching processes with immigration and the wright hypergeometric functions. Preprint (2007). Math. Review number not available.
- M. R. Pistorius . On doubly reflected completely asymmetric Lévy processes. Stochastic Process. Appl. 107 (2003), no. 1, 131--143. MR1995924 (2004k:60137)
- M. R. Pistorius . On exit and ergodicity of the spectrally one-sided Lévy process reflected at its infimum. J. Theoret. Probab. 17 (2004), no. 1, 183--220. MR2054585 (2005e:60104)
- M. R. Pistorius . A potential-theoretical review of some exit problems of spectrally negative Lévy processes. Séminaire de Probabilités XXXVIII, 30--41, Lecture Notes in Math., 1857, Springer, Berlin, 2005. MR2126965 (2006k:60086)
- M. R. Pistorius . An excursion-theoretical approach to some boundary crossing problems and the Skorokhod embedding for reflected Lévy processes. Séminaire de Probabilités XL, 287--307, Lecture Notes in Math., 1899, Springer, Berlin, 2007. MR2409012
- H. Pollard . The completely monotonic character of the Mittag-Leffler function $Esb a(-x)$. Bull. Amer. Math. Soc. 54, (1948). 1115--1116. MR0027375 (10,295e)
- J. F. Renaud ; X. Zhou . Distribution of the present value of dividend payments in a Lévy risk model. J. Appl. Probab. 44 (2007), no. 2, 420--427. MR2340208
- L. C. G. Rogers . The two-sided exit problem for spectrally positive Lévy processes. Adv. in Appl. Probab. 22 (1990), no. 2, 486--487. MR1053243 (93f:60110)
- J. Rosinski . Tempering stable processes. Stochastic Process. Appl. 117 (2007), no. 6, 677--707. MR2327834 (2008g:60146)
- K. Sato . Lévy processes and infinitely divisible distributions. Translated from the 1990 Japanese original. Revised by the author. Cambridge Studies in Advanced Mathematics, 68. Cambridge University Press, Cambridge, 1999. xii+486 pp. ISBN: 0-521-55302-4 MR1739520 (2003b:60064)
- W. R. Schneider Completely monotone generalized Mittag-Leffler functions. Exposition. Math. 14 (1996), no. 1, 3--16. MR1382012 (97a:33041)
- R. Song ; Z. Vondracek . Potential theory of special subordinators and subordinate killed stable processes. J. Theoret. Probab. 19 (2006), no. 4, 817--847. MR2279605 (2008g:60237)
- R. Song ; Z. Vondracek . Potential theory of subordinate Brownian motion. Lecture notes (2007). Math. Review number not available.
- R. Song ; Z. Vondracek . Some remarks on special subordinators. To appear in Rocky Mountain Journal of Mathematics (2008). Math. Review number not available.
- V. N. Suprun . The ruin problem and the resolvent of a killed independent increment process. (Russian) Ukrain. Mat. v Z. 28 (1976), no. 1, 53--61, 142. MR0428476 (55 #1497)
- L. Takács . Combinatorial methods in the theory of stochastic processes. Reprint of the 1967 original. Robert E. Krieger Publishing Co., Huntington, N. Y., 1977. xi+262 pp. MR0431313 (55 #4314)
- O. Thorin . On the infinite divisibility of the lognormal distribution. Scand. Actuar. J. (1977) no. 3, 121--148. MR0552135 (80m:60022)
- V. Vigon . Votre Lévy rampe-t-il? (French) [Does your Levy process creep?] J. London Math. Soc. (2) 65 (2002), no. 1, 243--256. MR1875147 (2002i:60101)
- V. M. Zolotarev . The moment of first passage of a level and the behaviour at infinity of a class of processes with independent increments. (Russian) Teor. Verojatnost. i Primenen. 9 (1964) 724--733. MR0171315 (30 #1546)

This work is licensed under a Creative Commons Attribution 3.0 License.