Pathwise approximations of processes based on the fine structure of their filtrations

Walter Willinger; Murad S. Taqqu

Séminaire de probabilités de Strasbourg (1988)

  • Volume: 22, page 542-599

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Willinger, Walter, and Taqqu, Murad S.. "Pathwise approximations of processes based on the fine structure of their filtrations." Séminaire de probabilités de Strasbourg 22 (1988): 542-599. <http://eudml.org/doc/113654>.

@article{Willinger1988,
author = {Willinger, Walter, Taqqu, Murad S.},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {pathwise approximations of processes; skeletons; filtration; pathwise convergence; natural convergence; examples; skeleton approximation; Brownian motion},
language = {fre},
pages = {542-599},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Pathwise approximations of processes based on the fine structure of their filtrations},
url = {http://eudml.org/doc/113654},
volume = {22},
year = {1988},
}

TY - JOUR
AU - Willinger, Walter
AU - Taqqu, Murad S.
TI - Pathwise approximations of processes based on the fine structure of their filtrations
JO - Séminaire de probabilités de Strasbourg
PY - 1988
PB - Springer - Lecture Notes in Mathematics
VL - 22
SP - 542
EP - 599
LA - fre
KW - pathwise approximations of processes; skeletons; filtration; pathwise convergence; natural convergence; examples; skeleton approximation; Brownian motion
UR - http://eudml.org/doc/113654
ER -

References

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  1. Aldous, D.J. (1981), Weak Convergence and the Theory of Processes, (unpublished) monograph, University of California, Berkeley. 
  2. Billingsley, P. (1968), Convergence of Probability Measures, J. Wiley, New York. Zbl0172.21201
  3. Billingsley, P. (1979), Probability and Measure, J. Wiley, New York. Zbl0411.60001
  4. Clark, J.M.C. (1970), The representation of functionals of Brownian motion by stochastic integrals, Ann. Math. Statist.41, 1282-1295; correction ibid. 42 (1971), 1778. Zbl0213.19402
  5. Dellacherie, C. (1975), Integrales stochastique par rapport aux processus de Wiener et de Poisson, in: Sem. Probab.VIII,Lecture Notes in Mathematics381, Springer-Verlag, Berlin-Heidelberg-New York, 25-26; see also Sem. Probab.IX, Lecture Notes in Mathematics465, Springer-Verlag, Berlin-Heidelberg-New York (1975), 495. Zbl0302.60049
  6. Dellacherie, C. and Meyer, P.-A. (1978), Probabilities and Potential A, North-Holland, Amsterdam. Zbl0494.60001
  7. Dellacherie, C. and Meyer, P.-A. (1982), Probabilities and Potential B, North-Holland, Amsterdam. Zbl0494.60002
  8. Dubins, L.E. (1968), On a problem of Skorohod, Ann. Math. Statist.39, 2094-2097. Zbl0185.45103
  9. Duffle, D. and Huang, C. (1985), Implementing Arrow-Debreu equilibria by continuous trading of few long-lived securities, Econometrica53, 1337-1356. Zbl0576.90014
  10. Fisk, D. (1965), Quasi-Martingales, Trans. Amer. Math. Soc.120, 369-389. Zbl0133.40303
  11. Harrison, J.M.and Pliska, S.R. (1981), Martingales and stochastic integrals in the theory of continuous trading, Stoch. Proc. Appl.11, 215-260. Zbl0482.60097
  12. Harrison, J.M.and Pliska, S.R. (1983), A stochastic calculus model of continuous trading: Complete markets, Stoch. Proc. Appl.15, 313-316. Zbl0511.60094
  13. Huang, C. (1985), Information structure and equilibrium asset prices, J. Econom. Theory35, 33-71. Zbl0553.90027
  14. Itô, K. (1951), Multiple Wiener integral, J. Math. Soc. Japan3, 151-169. Zbl0044.12202
  15. Itô, K. and McKean, H.P., Jr. (1965), Diffusion Processes and Their Sample Paths, Die Grundlehren der Math. Wissenschaften, Bd. 125, Springer-Verlag, Berlin-Heidelberg-NewYork. Zbl0127.09503
  16. Knight, F.B. (1981), Essentials of Brownian motion and diffusions, Math. Surveys 18, Amer. Math. Soc., Providence, Rhode Island. Zbl0458.60002
  17. Kreps, D.M. (1982), Multiperiod securities and the efficient allocation of risk: A comment on the Black-Scholes option pricing model, in: The Economics of Uncertainty and Information (J. McCall, Ed.), Univ. of Chicago Press. 
  18. Kunita, H. and Watanabe, S. (1967), On square integrable martingles, Nagoya Math. J.30, 209-245. Zbl0167.46602
  19. Meyer, P.-A. (1971), Sur un article de Dubins, in: Sem. Probab. V, Lecture Notes in Mathematics191, Spriner-Verlag, Berlin-Heidelberg-New York, 170-176. 
  20. Rockafellar, R.T. (1970), Convex Analysis, Princeton Univ. Press, Princeton. Zbl0193.18401
  21. Taqqu, M.S.and Willinger, W. (1987), The analysis of finite security markets using martingales, Adv. Appl. Prob.19, 1-25. Zbl0618.60047
  22. Willinger, W. and Taqqu, M.S. (1987), Pathwise stochastic integration and applications to the theory of continuous trading, Bell Communications Research, Tech. Memorandum. Zbl0698.60043
  23. Willinger, W. (1987), Pathwise stochastic integration and almost-sure approximation of stochastic processes, Ph.D. Thesis, School of Operations Research and Industrial Engineering, Cornell University, Ithaca. 

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