Lévy processes that can creep downwards never increase

 Access to full text

 Full (PDF)

1. [Ad] O. Adelman, Brownian motion never increases: A new proof to a result of Dvoretzky, Erdös and Kakutani, Israël J. Math., Vol. 50, 1985, pp. 189-192. Zbl0573.60030MR793851
2. [Al] D.J. Aldous, Probability Approximation via the Poisson Clumping Heuristic, Springer, New York, 1989. Zbl0679.60013MR969362
3. [Be] J. Bertoin, Increase of a Lévy process with no positive jumps, Stochastics, Vol. 37, 1991, pp. 247-251. Zbl0739.60065MR1149349
4. [Bi] N.H. Bingham, Fluctuation theory in continuous time, Adv. Appl. Prob., Vol. 7, 1975, pp. 705-766. Zbl0322.60068MR386027
5. [Bu] C. Burdzy, On nonincrease of Brownian motion, Ann. Prob., Vol. 18, 1990, pp. 978-980. Zbl0719.60086MR1062055
6. [C-W] K.L. Chung and J.B. Walsh, To reverse a Markov process, Acta Mathematica, Vol. 123, 1969, pp. 225-251. Zbl0187.41302MR258114
7. [D-E-K] A. Dvoretzky, P. Erdös and S. Kakutani, On nonincrease everywhere of the Brownian motion process, in: Proc. 4th. Berkeley Symp. Math. Stat. and Probab., Vol. II, 1961, pp. 103-116. Zbl0111.15002MR132608
8. [Fr] B. Fristedt, Sample functions of stochastic processes with stationary independent increments, in: P. NEY and S. PORT Ed., Adv. Probab., Vol. 3, 1974, pp. 241-396, Dekker. Zbl0309.60047MR400406
9. [G-P] P. Greenwood and J. Pitman, Fluctuation identities for Lévy processes and splitting at the maximum, Adv. Appl. Prob., Vol. 12, 1980, pp. 893-902. Zbl0443.60037MR588409
10. [Ke] H. Kesten, Hitting probabilities of single points for processes with stationary independent increments, Mem. Amer. Math. Soc., Vol. 93, 1969. Zbl0186.50202MR272059
11. [Kn] F.B. Knight, Essential of Brownian Notion and Diffusion, Math Survey, Vol. 18, Amer. Math. Soc., 1981, Providence, R.I. Zbl0458.60002MR613983
12. [Mi-1] P.W. Millar, Exit properties of stochastic processes with stationary independent increments, Trans. Amer. Math. Soc., Vol. 178, 1973, pp. 459-479. Zbl0268.60065MR321198
13. [Mi-2] P.W. Millar, Zero-one laws and the minimum of a Markov process, Trans. Amer. Math. Soc., Vol. 226, 1977, pp. 365-391. Zbl0381.60062MR433606
14. [Ne] J. Neveu, Une généralisation des processus à accroissements positifs indépendants, Abh. Math. Sem. Univ. Hamburg, Vol. 25, 1961, pp. 36-61. Zbl0103.36303MR130714
15. [Ro] L.C.G. Rogers, A new identity for real Lévy processes, Ann. Inst. Henri-Poincaré, Vol. 20, 1984, pp. 20-34. MR740248
16. [Sh] M.J. Sharpe, General Theory of Markov Processes, Academic Press, Boston, 1989. Zbl0649.60079MR958914
17. [Wi] D. Williams, Path decomposition and continuity of local time for one-dimensional diffusions, Proc. London Math. Soc., Vol. 28, 1974, pp. 738-768. Zbl0326.60093MR350881