Itô formula for an asymptotically 4-stable process

Annals of Applied Probability

Volumn 6, Issue 1, 1996, Pages 200-217

  Burdzy, Krzysztof ^a   Ma̧drecki, Andrzej ^b  

^a UNIVERSITY OF WASHINGTON   (United States)

^b WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

4 stable process; It formula; Stable process

Indexed keywords

EID: 0040204047     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1034968071     Document Type: Article

References (16)

1. ANTOSIEWICZ, P., MIKUSIŃSKI, J. and SIKORSKI, R. (1973). Theory of Distributions (The Sequential Approach). North-Holland, Amsterdam.
2. BURDZY, K. (1993). Some path properties of iterated Brownian motion. In Seminar on Stochastic Processes 1992 (E. Çinlar, K. L. Chung and M. Sharpe, eds.) 67-87. Birkhäuser, Boston.
3. BURDZY, K. (1994). Variation of iterated Brownian motion. In Measure-Valued Processes, Stochastic Partial Differential Equations and Interacting Systems (D. A. Dawson, ed.) 35-53. Amer. Math. Soc., Providence, RI.
4. BURDZY, K. and MA̧DRECKI, A. (1995). An asymptotically 4-stable process. J. Fourier Anal. Appl. Special Issue. Proceedings of the Conference in Honor of J.-P. Kahane 97-117.
5. FUNAKI, T. (1979). Probabilistic construction of the solution of some higher order parabolic differential equations. Proc. Japan Acad. Ser. A Math. Sci. 55 176-179.
6. HELMS, L. L. (1967). Biharmonic functions and Brownian motion. J. Appl. Probab. 4 130-136.
7. HOCHBERG, K. J. (1978). A signed measure on path space related to Wiener measure. Ann. Probab. 6 433-458.
8. HOCHBERG, K. J. and ORSINGHER, E. (1994). The arc-sine law and its analogues for processes governed by signed and complex measures. Stochastic Process. Appl. To appear.
9. 2q. Soviet Math. Dokl. 1 760-763.
10. MA̧DRECKI, A. and RYBACZUK, M. (1989). On a Feynman-Kac formula. In Stochastic Methods in Experimental Sciences. Proceedings of COSMEX Conference 1989 (W. Kasprzak and A. Weron, eds.) 312-321. World Scientific, Singapore.
11. MA̧DRECKI, A. and RYBACZUK, M. (1993). New Feynman-Kac type formula. Rep. Math. Phys. 32 301-327.
12. NISHIOKA, K. (1985). Stochastic calculus for a class of evolution equations. Japan J. Math. (N.S.) 11 59-102.
13. NISHIOKA, K. (1987). A stochastic solution of a high order parabolic equation. J. Math. Soc. Japan 39 209-231.
14. NISHIOKA, K. (1994). The first hitting time and place of a biharmonic pseudo process. Preprint.
15. SAINTY, PH. (1992). Construction of a complex-valued fractional Brownian motion of order N. J. Math. Phys. 33 3128-3149.
16. VAINSTEIN, A. I., ZAKHAROV, V. I., NOVIKOV, V. A. and SHIFMAN, M. A. (1982). ABC of instantons. Uspekhi Fiz. Nauk 136 553-591.