On solutions of one-dimensional stochastic differential equations driven by stable Lévy motion

Stochastic Processes and their Applications

Volumn 68, Issue 2, 1997, Pages 209-228

  Zanzotto, P A ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

"Local" existence; 0 1 Law; Existence; Purely discontinuous martingales; Random measures; Stable integrals; Stochastic differential equations; Time change; Stable L vy motions

Indexed keywords

EID: 0031575032     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(97)00030-6     Document Type: Article

References (18)

1. Blumenthal, R.M., Getoor, R.K. 1968. Markov Processes and Potential Theory. Academic Press, New York.
2. Boylan, E.S., 1964. Local times for a class of Markov processes. Illinois J. Math, 8, 19-39.
3. Dellacherie, C., 1972. Capacités et Processus Stochastiques. Springer, Berlin.
4. Dellacherie, C., Meyer, P.A., 1980. Probabilités et Potentiel, Chap. V à VIII, Hermann, Paris.
5. Engelbert, H.J., Schmidt, W., 1981. On the behaviour of certain functionals of the Wiener process and applications to stochastic differential equations. in: Lectures Notes in Control and Information Sciences, vol. 36. Springer, Berlin, pp. 47-55.
6. Engelbert, H.J., Schmidt, W., 1985. On solutions of one-dimensional stochastic differential equations without drift. Z. Wahrscheinlichkeits. verw. Geb. 68, 287-314.
7. Jacod, J., 1979. Calcul Stochastique et Problèmes de Martingales. Lecture Notes in Math., vol. 714. Springer, Berlin.
8. Jacod, J., Shiryaev, A.N., 1987. Limit Theorems for Stochastic Processes. Springer, Berlin.
9. Kallenberg, O., 1992. Some time change representations of stable integrals, via predictable transformations of local martingales. Stoch. Process. Appl. 40, 199-223.
10. Karatzas, I., Shreve, S.E., 1994. Brownian Motion and Stochastic Calculus, 2nd ed. Springer, New York.
11. Kesten, H., 1969. Hitting probabilities of single points for processes with stationary, independent increments. Mem. Amer. Math. Soc., vol. 93, Providence, RI, 1-129.
12. Komatsu, T., 1984. On the martingale problem for generators of stable processes with perturbations. Osaka J. Math. 21, 113-132.
13. Port, S.C., 1967. Hitting times and potentials for recurrent stable processes. J. d'Anal. Math. 20, 371-395.
14. Rosiński, J., Woyczyński, W.A., 1986. On Itô stochastic integration with respect to p-stable motion: inner clock, integrability of sample paths, double and multiple integrals. Ann. Probab. 14, 271-286.
15. Royden, H.L., 1968. Real Analysis. 2nd ed. Macmillan, New York.
16. Samorodnitsky, G., Taqqu, M.S., 1994. Stable Non-Gaussian Random Processes - Stochastic Models with Infinite Variance. Chapman & Hall, New York.
17. Stone, Ch., 1963. The set of zeros of a semistable process. Illinois J. Math. 7, 631-637.
18. Zolotarev, V.M., 1986. One-dimensional Stable Distributions. Translations of Mathematical Monographs, vol. 65, American Mathematical Society, Providence, RI.