References

• Alvarez, Luis H. R. On the properties of $r$-excessive mappings for a class of diffusions. Ann. Appl. Probab. 13 (2003), no. 4, 1517--1533. MR2023887
• Alvarez, Luis H. R. A class of solvable impulse control problems. Appl. Math. Optim. 49 (2004), no. 3, 265--295. MR2041852
• Alvarez, Luis H. R. A class of solvable stopping games. Appl. Math. Optim. 58 (2008), no. 3, 291--314. MR2456849
• Bassan, Bruno; Ceci, Claudia. Optimal stopping problems with discontinuous reward: regularity of the value function and viscosity solutions. Stoch. Stoch. Rep. 72 (2002), no. 1-2, 55--77. MR1896437
• Beibel, M.; Lerche, H. R. A new look at optimal stopping problems related to mathematical finance. Empirical Bayes, sequential analysis and related topics in statistics and probability (New Brunswick, NJ, 1995). Statist. Sinica 7 (1997), no. 1, 93--108. MR1441146
• Beibel, M.; Lerche, H. R. A note on optimal stopping of regular diffusions under random discounting. Teor. Veroyatnost. i Primenen. 45 (2000), no. 4, 657--669; translation in Theory Probab. Appl. 45 (2002), no. 4, 547--557 MR1968720
• Bensoussan, Alain; Lions, Jacques-Louis. Applications of variational inequalities in stochastic control. Translated from the French. Studies in Mathematics and its Applications, 12. North-Holland Publishing Co., Amsterdam-New York, 1982. xi+564 pp. ISBN: 0-444-86358-3 MR0653144
• Borodin, Andrei N.; Salminen, Paavo. 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
• Breiman, Leo. Probability. Corrected reprint of the 1968 original. Classics in Applied Mathematics, 7. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992. xiv+421 pp. ISBN: 0-89871-296-3 MR1163370
• Christensen, Sören; Irle, Albrecht. A harmonic function technique for the optimal stopping of diffusions. Stochastics 83 (2011), no. 4-6, 347--363. MR2842584
• Çinlar, E.; Jacod, J.; Protter, P.; Sharpe, M. J. Semimartingales and Markov processes. Z. Wahrsch. Verw. Gebiete 54 (1980), no. 2, 161--219. MR0597337
• Dayanik, Savas. Optimal stopping of linear diffusions with random discounting. Math. Oper. Res. 33 (2008), no. 3, 645--661. MR2442645
• Dayanik, Savas; Karatzas, Ioannis. On the optimal stopping problem for one-dimensional diffusions. Stochastic Process. Appl. 107 (2003), no. 2, 173--212. MR1999788
• Dynkin, E. B. Optimal choice of the stopping moment of a Markov process. (Russian) Dokl. Akad. Nauk SSSR 150 1963 238--240. MR0154329
• Dynkin, E. B. The exit space of a Markov process. (Russian) Uspehi Mat. Nauk 24 1969 no. 4 (148) 89--152. MR0264768
• Dynkin, E. B. Markov processes. Vols. I, II. Translated with the authorization and assistance of the author by J. Fabius, V. Greenberg, A. Maitra, G. Majone. Die Grundlehren der Mathematischen Wissenschaften, Bände 121, 122 Academic Press Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg 1965 Vol. I: xii+365 pp.; Vol. II: viii+274 pp. MR0193671
• El~Karoui, N.: Les aspects probabilistes du contrôle stochastique. phNinth Saint Flour Probability Summer School--1979 (Saint Flour, 1979), pp. 73--238, Lecture Notes in Math., 876, phSpringer, Berlin-New York, 1981. MR0637471
• Friedman, Avner. Stochastic differential equations and applications. Two volumes bound as one. Reprint of the 1975 and 1976 original published in two volumes. Dover Publications, Inc., Mineola, NY, 2006. xvi+531 pp. ISBN: 0-486-45359-6 MR2295424
• Gapeev, Pavel V.; Lerche, Hans Rudolf. On the structure of discounted optimal stopping problems for one-dimensional diffusions. Stochastics 83 (2011), no. 4-6, 537--554. MR2842594
• Itô, Kiyosi; McKean, Henry 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
• Johnson, Timothy C.; Zervos, Mihail. The solution to a second order linear ordinary differential equation with a non-homogeneous term that is a measure. Stochastics 79 (2007), no. 3-4, 363--382. MR2308081
• Karatzas, Ioannis; Shreve, Steven E. Brownian motion and stochastic calculus. Graduate Texts in Mathematics, 113. Springer-Verlag, New York, 1988. xxiv+470 pp. ISBN: 0-387-96535-1 MR0917065
• Karlin, Samuel; Taylor, Howard M. A second course in stochastic processes. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. xviii+542 pp. ISBN: 0-12-398650-8 MR0611513
• Krylov, N. V. Controlled diffusion processes. Translated from the Russian by A. B. Aries. Applications of Mathematics, 14. Springer-Verlag, New York-Berlin, 1980. xii+308 pp. ISBN: 0-387-90461-1 MR0601776
• Kunita, Hiroshi; Watanabe, Takesi. Markov processes and Martin boundaries. I. Illinois J. Math. 9 1965 485--526. MR0181010
• Lamberton, Damien. Optimal stopping with irregular reward functions. Stochastic Process. Appl. 119 (2009), no. 10, 3253--3284. MR2568273
• Lempa, Jukka. A note on optimal stopping of diffusions with a two-sided optimal rule. Oper. Res. Lett. 38 (2010), no. 1, 11--16. MR2565808
• Lerche, Hans Rudolf; Urusov, Mikhail. Optimal stopping via measure transformation: the Beibel-Lerche approach. Stochastics 79 (2007), no. 3-4, 275--291. MR2308076
• Meyer, Paul-André. Fonctionelles multiplicatives et additives de Markov. (French) Ann. Inst. Fourier (Grenoble) 12 1962 125--230. MR0140148
• Øksendal, Bernt. Stochastic differential equations. An introduction with applications. Sixth edition. Universitext. Springer-Verlag, Berlin, 2003. xxiv+360 pp. ISBN: 3-540-04758-1 MR2001996
• Øksendal, Bernt; Reikvam, Kristin. Viscosity solutions of optimal stopping problems. Stochastics Stochastics Rep. 62 (1998), no. 3-4, 285--301. MR1613260
• Peskir, Goran; Shiryaev, Albert. Optimal stopping and free-boundary problems. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel, 2006. xxii+500 pp. ISBN: 978-3-7643-2419-3; 3-7643-2419-8 MR2256030
• Presman, E.: Solution of the optimal stopping problem for one-dimensional diffusion based on a modification of the payoff function. phProkhorov and Contemporary Probability Theory, In Honor of Yuri V. Prokhorov, A. N. Shiryaev, S. R. S. Varadhan and E. L. Presman, eds. Springer Proceedings in Mathematics & Statistics, 33. phSpringer-Verlag, Berlin-Heidelberg, 2013.
• Revuz, D. Mesures associées aux fonctionnelles additives de Markov. I. (French) Trans. Amer. Math. Soc. 148 1970 501--531. MR0279890
• Revuz, Daniel; Yor, Marc. Continuous martingales and Brownian motion. Second edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 293. Springer-Verlag, Berlin, 1994. xii+560 pp. ISBN: 3-540-57622-3 MR1303781
• Rüschendorf, Ludger; Urusov, Mikhail A. On a class of optimal stopping problems for diffusions with discontinuous coefficients. Ann. Appl. Probab. 18 (2008), no. 3, 847--878. MR2418231
• Salminen, P. Optimal stopping of one-dimensional diffusions. Math. Nachr. 124 (1985), 85--101. MR0827892
• Shiryaev, A. N. Optimal stopping rules. Translated from the 1976 Russian second edition by A. B. Aries. Reprint of the 1978 translation. Stochastic Modelling and Applied Probability, 8. Springer-Verlag, Berlin, 2008. xii+217 pp. ISBN: 978-3-540-74010-0 MR2374974