Tightness of probability measures in D([0, T]; C) and D([0, T]; D)

Hiroshi KUNITA

doi:10.2969/jmsj/03820309

Hiroshi KUNITA

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JOURNAL FREE ACCESS

1986 Volume 38 Issue 2 Pages 309-334

DOI https://doi.org/10.2969/jmsj/03820309

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Published: 1986 Received: June 08, 1984 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) P. Billingsley, Convergence of probability measures, John Wiley and Sons, New York, 1968.
2) N. N. Chentsov, Weak convergence of stochastic processes whose trajectories have no discontinuities of the second kind and the “heuristic” approach to the Kolmogorov-Smirnov tests, Theory Probab. Appl., 1 (1957), 140-144.
3) N. N. Chentsov, Limit theorems for some classes of random functions, Proc. All-Union Conf. Theory Prob. and Math. Statist. (Erevan, 1958), Selected Transl. Math. Statist. and Prob., 9 (1970), 37-42.
4) H. Cramer and M. R. Leadbetter, Stationary and related processes, John Wiley and Sons, New York, 1967.
5) T. Fujiwara and H. Kunita, Stochastic differential equations of jump type and Lévy processes in diffeomorphisms group, J. Math. Kyoto Univ., 25 (1985), 71-106.
6) A. M. Garsia, Continuity properties of Gaussian processes with multidimensional time parameter, Proc. Sixth Berkeley Symp. on Math. Stat. and Prob., 2 (1972), 369-374.
7) N. Kono, Real variable lemmas and their applications to sample properties of stochastic processes, J. Math. Kyoto Univ., 19 (1981), 413-433.
8) T. G. Kurtz, Approximation of population processes, CBNS-NSF Regional Conference Series in Appl. Math., 1981.
9) H. Totoki, A method of construction of measures on function spaces and its applications to stochastic processes, Mem. Fac. Sci. Kyushu Univ. Ser. A Math., 15 (1961), 178-190.
10) H. Kunita, Convergence of stochastic flows with jumps and Lévy processes in diffeomorphisms group, to appear in Ann. Inst. H. Poincaré.

Right : [1] P. Billingsley, Convergence of probability measures, John Wiley and Sons, New York, 1968.
[2] N. N. Chentsov, Weak convergence of stochastic processes whose trajectories have no discontinuities of the second kind and the “heuristic” approach to the Kolmogorov-Smirnov tests, Theory Probab. Appl., 1 (1957), 140-144.
[3] N. N. Chentsov, Limit theorems for some classes of random functions, Proc. All-Union Conf. Theory Prob. and Math. Statist. (Erevan, 1958), Selected Transl. Math. Statist. and Prob., 9 (1970), 37-42.
[4] H. Cramer and M. R. Leadbetter, Stationary and related processes, John Wiley and Sons, New York, 1967.
[5] T. Fujiwara and H. Kunita, Stochastic differential equations of jump type and Lévy processes in diffeomorphisms group, J. Math. Kyoto Univ., 25 (1985), 71-106.
[6] A. M. Garsia, Continuity properties of Gaussian processes with multidimensional time parameter, Proc. Sixth Berkeley Symp. on Math. Stat. and Prob., 2 (1972), 369-374.
[7] N. Kôno, Real variable lemmas and their applications to sample properties of stochastic processes, J. Math. Kyoto Univ., 19 (1981), 413-433.
[8] T. G. Kurtz, Approximation of population processes, CBNS-NSF Regional Conference Series in Appl. Math., 1981.
[9] H. Totoki, A method of construction of measures on function spaces and its applications to stochastic processes, Mem. Fac. Sci. Kyushu Univ. Ser. A Math., 15 (1961), 178-190.
[10] H. Kunita, Convergence of stochastic flows with jumps and Lévy processes in diffeomorphisms group, to appear in Ann. Inst. H. Poincaré.

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