A characterization of the multiparameter Wiener process and an application
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- by Chang C. Y. Dorea PDF
- Proc. Amer. Math. Soc. 85 (1982), 267-271 Request permission
Abstract:
In this note we give an application of a characterization of the multiparameter Wiener process and of the invariance principle for ${R^k}$-valued martingales.References
- P. J. Bickel and M. J. Wichura, Convergence criteria for multiparameter stochastic processes and some applications, Ann. Math. Statist. 42 (1971), 1656–1670. MR 383482, DOI 10.1214/aoms/1177693164
- Patrick Billingsley, The Lindeberg-Lévy theorem for martingales, Proc. Amer. Math. Soc. 12 (1961), 788–792. MR 126871, DOI 10.1090/S0002-9939-1961-0126871-X
- Patrick Billingsley, Convergence of probability measures, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0233396
- R. Cairoli and John B. Walsh, Stochastic integrals in the plane, Acta Math. 134 (1975), 111–183. MR 420845, DOI 10.1007/BF02392100
- M. Deo Chandrakant, A functional central limit theorem for stationary random fields, Ann. Probability 3 (1975), no. 4, 708–715. MR 375410, DOI 10.1214/aop/1176996310 E. B. Dynkin, Markov processes, Springer-Verlag, Berlin, 1965.
- Thomas G. Kurtz, Semigroups of conditioned shifts and approximation of Markov processes, Ann. Probability 3 (1975), no. 4, 618–642. MR 383544, DOI 10.1214/aop/1176996305
- D. L. McLeish, Dependent central limit theorems and invariance principles, Ann. Probability 2 (1974), 620–628. MR 358933, DOI 10.1214/aop/1176996608
- Galen R. Shorack and R. T. Smythe, Inequalities for $\textrm {max}\mid S_{\textbf {k}}\mid /b_{\textbf {k}}$ where $\textbf {k}\in N^{r}$, Proc. Amer. Math. Soc. 54 (1976), 331–336. MR 400386, DOI 10.1090/S0002-9939-1976-0400386-4
- H. F. Trotter, An elementary proof of the central limit theorem, Arch. Math. 10 (1959), 226–234. MR 108847, DOI 10.1007/BF01240790
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 85 (1982), 267-271
- MSC: Primary 60F17
- DOI: https://doi.org/10.1090/S0002-9939-1982-0652455-4
- MathSciNet review: 652455