References

• Bingham, N. H.; Goldie, C. M.; Teugels, J. L. Regular variation. Encyclopedia of Mathematics and its Applications, 27. Cambridge University Press, Cambridge, 1989. xx+494 pp. ISBN: 0-521-37943-1 MR1015093
• Borodin, A.N.; Salminen, P. Handbook of Brownian motion—facts and formulae. Second edition. Probability and its Applications. Birkhäuser Verlag, Basel, 2002. xvi+672 pp. ISBN: 3-7643-6705-9 MR1912205
• Biane, Ph.; Yor, M. Valeurs principales associées aux temps locaux browniens. (French) [Principal values associated with Brownian local times] Bull. Sci. Math. (2) 111 (1987), no. 1, 23--101. MR0886959
• Čistjakov, V. P. A theorem on sums of independent positive random variables and its applications to branching random processes. (Russian) Teor. Verojatnost. i Primenen 9 1964 710--718. MR0170394
• Dym, H.; McKean, H. P. Gaussian processes, function theory, and the inverse spectral problem. Probability and Mathematical Statistics, Vol. 31. Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. xi+335 pp. MR0448523
• Embrechts, P.; Goldie, C. M.; Veraverbeke, Noël. Subexponentiality and infinite divisibility. Z. Wahrsch. Verw. Gebiete 49 (1979), no. 3, 335--347. MR0547833
• Feller, W. An introduction to probability theory and its applications. Vol. II. Second edition John Wiley & Sons, Inc., New York-London-Sydney 1971 xxiv+669 pp. MR0270403
• Itô, K.; McKean, H. P., Jr. Diffusion processes and their sample paths. Second printing, corrected. Die Grundlehren der mathematischen Wissenschaften, Band 125. Springer-Verlag, Berlin-New York, 1974. xv+321 pp. MR0345224
• Kasahara, Y. Spectral theory of generalized second order differential operators and its applications to Markov processes. Japan. J. Math. (N.S.) 1 (1975/76), no. 1, 67--84. MR0405615
• Kac, I. S.; Krein, M. G. On the spectral functions of the string. Am. Math. Soc., Translat., II. Ser., 103:19--102, 1974.
• Knight, F. B. Characterization of the Levy measures of inverse local times of gap diffusion. Seminar on Stochastic Processes, 1981 (Evanston, Ill., 1981), pp. 53--78, Progr. Prob. Statist., 1, Birkhäuser, Boston, Mass., 1981. MR0647781
• Kotani, S.; Watanabe, S. Kreĭn's spectral theory of strings and generalized diffusion processes. Functional analysis in Markov processes (Katata/Kyoto, 1981), pp. 235--259, Lecture Notes in Math., 923, Springer, Berlin-New York, 1982. MR0661628
• Meyer, P.-A. Probabilités et potentiel. (French) Publications de l'Institut de Mathématique de l'Université de Strasbourg, No. XIV. Actualités Scientifiques et Industrielles, No. 1318 Hermann, Paris 1966 320 pp. MR0205287
• Millar, P. W. Random times and decomposition theorems. Probability (Proc. Sympos. Pure Math., Vol. XXXI, Univ. Illinois, Urbana, Ill., 1976), pp. 91--103. Amer. Math. Soc., Providence, R. I., 1977. MR0443109
• Najnudel, J.; Roynette, B.; Yor, M. A global view of Brownian penalisations. MSJ Memoirs, 19. Mathematical Society of Japan, Tokyo, 2009. xii+137 pp. ISBN: 978-4-931469-52-5 MR2528440
• Profeta, C. Penalization of a positively recurrent diffusion by an exponential function of its local time. Publ. Res. Inst. Math. Sci. 46 (2010), no. 3, 681--718. MR2760742
• Profeta, C.; Roynette, B.; Yor, M. Option prices as probabilities. A new look at generalized Black-Scholes formulae. Springer Finance. Springer-Verlag, Berlin, 2010. xxii+270 pp. ISBN: 978-3-642-10394-0 MR2582990
• Pitman, J.; Yor, M. Laplace transforms related to excursions of a one-dimensional diffusion. Bernoulli 5 (1999), no. 2, 249--255. MR1681697
• Roynette, B.; Vallois, P.; Yor, M. Limiting laws associated with Brownian motion perturbed by normalized exponential weights. I. Studia Sci. Math. Hungar. 43 (2006), no. 2, 171--246. MR2229621
• Roynette, B.; Vallois, P.; Yor, M. Limiting laws associated with Brownian motion perturbed by its maximum, minimum and local time. II. Studia Sci. Math. Hungar. 43 (2006), no. 3, 295--360. MR2253307
• Roynette, B.; Vallois, P.; Yor, M. Some penalisations of the Wiener measure. Jpn. J. Math. 1 (2006), no. 1, 263--290. MR2261065
• Roynette, B.; Yor, M. Penalising Brownian paths. Lecture Notes in Mathematics, 1969. Springer-Verlag, Berlin, 2009. xiv+275 pp. ISBN: 978-3-540-89698-2 MR2504013
• Salminen, P. One-dimensional diffusions and their exit spaces. Math. Scand. 54 (1984), no. 2, 209--220. MR0757463
• Salminen, P. On the distribution of supremum of diffusion local time. Statist. Probab. Lett. 18 (1993), no. 3, 219--225. MR1241618
• Salminen, P. A pointwise limit theorem for the transition density of a linear diffusion. In Frontiers in pure and applied probability II. Proceedings of the fourth Russian-Finnish symposium on probability theory and mathematical statistics. Moscow (Russia), October 3-8, 1993., pages 171--176. Moskva: TVP, 1996.
• Salminen, P. On last exit decompositions of linear diffusions. Studia Sci. Math. Hungar. 33 (1997), no. 1-3, 251--262. MR1454113
• Sato, K. 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
• Salminen, P.; Vallois, P. On subexponentiality of the Lévy measure of the diffusion inverse local time; with applications to penalizations. Electron. J. Probab. 14 (2009), no. 67, 1963--1991. MR2540855
• Salminen, P.; Vallois, P.; Yor, M. On the excursion theory for linear diffusions. Jpn. J. Math. 2 (2007), no. 1, 97--127. MR2295612
• Yano, K.; Yano, Y.; Yor, M. Penalising symmetric stable Lévy paths. J. Math. Soc. Japan 61 (2009), no. 3, 757--798. MR2552915