Feynman-Kac Penalisations of Symmetric Stable Processes

Masayoshi Takeda (Tohoku University, Mathematical Institute)

Abstract


In K. Yano, Y. Yano and M. Yor (2009), limit theorems for the one-dimensional symmetric α-stable process normalized by negative (killing) Feynman-Kac functionals were studied. We consider the same problem and extend their results to positive Feynman-Kac functionals of multi-dimensional symmetric α-stable processes.

Full Text: Download PDF | View PDF online (requires PDF plugin)

Pages: 32-43

Publication Date: February 10, 2010

DOI: 10.1214/ECP.v15-1524

References

  1. S. Albeverio, P. Blanchard and Z.M. Ma. Feynman-Kac semigroups in terms of signed smooth measures, "Random Partial Differential Equations" ed. U. Hornung et al., Birkhäuser, (1991). Math. Review 93i:60140
  2. M. Brancovan. Fonctionnelles additives speciales des processus recurrents au sens de Harris, Z. Wahrsch. Verw. Gebiete. 47 (1979) 163-194 . Math Review 80d:60096
  3. Z.-Q. Chen, P.J. Fitzsimmons, M. Takeda, J. Ying, and T.S. Zhang. Absolute continuity of symmetric Markov processes. Ann. Probab. 32 (2004), 2067-2098. Math Review 2005g:60121
  4. P.J. Fitzsimmons. Absolute continuity of symmetric diffusions. Ann. Probab. 25 (1997), 230-258. Math Review 98c:60097
  5. M. Fukushima, Y. Oshima and M. Takeda. Dirichlet Forms and Symmetric Markov Processes. Walter de Gruyter, Berlin (1994). Math Review 96f:60126
  6. J. Neveu. Potentiel Markovien recurrent des chaines de Harris. Ann. Inst. Fourier 22 (1972), 85-130. Math Review 52 #1889
  7. L. Rogers, D. Williams. Diffusions, Markov Processes, and Martingales. Vol. 2, John Wiley (1987). Math Review 89k:60117
  8. D. Revuz, M. Yor. Continuous Martingales and Brownian Motion. 3rd edition, Springer, New York (1998). Math Review 2000h:60050
  9. B. Roynette, P. Vallois, P. and M. Yor. Some penalisations of the Wiener measure. Jpn. J. Math. 1 (2006), 263-290. Math Review 2009b:60106
  10. B. Roynette, P. Vallois, and M. Yor. Limiting laws associated with Brownian motion perturbed by normalized exponential weights. I. Studia Sci. Math. Hungar. 43 (2006), 171-246. Math Review 2007e:60072
  11. P. Stollmann, J. Voigt. Perturbation of Dirichlet forms by measures, Potential Analysis 5 (1996), 109-138. Math Review 97e:47065
  12. M. Takeda. Exponential decay of lifetimes and a theorem of Kac on total occupation times. Potential Analysis 11 (1999), 235-247. Math Review 2000i:60084
  13. M. Takeda. Large deviations for additive functionals of symmetric stable processes. J. Theoret. Probab. 21 (2008), 336-355. Math Review 2009k:60175
  14. M. Takeda, K. Tsuchida. Differentiability of spectral functions for symmetric α-stable processes. Trans. Amer. Math. Soc. 359 (2007), 4031-4054. Math Review 2008a:35045
  15. M. Takeda, T. Uemura. Subcriticality and gaugeability for symmetric α-stable processes. Forum Math. 16 (2004), 505-517. Math Review 2005d:60124
  16. K. Yano, Y. Yano and M. Yor. Penalising symmetric stable Líevy paths. J. Math. Soc. Japan. 61 (2009), 757-798. Math Review number not available.
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.