随机过程及其局部时和随机场的极限定理
摘要
引文
[1] Borodin, A. N. (1982) , Distribution of integral functionals of Brownian motion. Zap. Naucn. Sem. Leningrad. Otdel. Mat. Inst.Steklova, 119: 19-38．
[2] Csaki, E. (1989) , An integral test for the supremum of Wiener local time. Probab. Th. Rel. Fields, 83:207-217．
[3] Csaki, E. and Foldes, A. (1986) , How small are the increments of the local time of a Wiener process? Ann. Probab., 14:533-546．
[4] Csaki, E.,Csorgo, M., Foldes, A. and Revesz, P. (1983) , How big are the increments of the local time of a Wiener process? Ann. Probab., 11:593-608．
[5] Einmahl, U. (1989) , The Darling-Erdos theorem for sums of i.i.d. random variables. Probab. Theory Relat. Fields, 82: 241-257．
[6] Feller, W. (1945) , The law of the iterated logarithm for identically distributed random variables. Ann. Math., 47: 631-638．
[7] Gut, A. and Spataru, A. (2000) , Precise asymptotics in the law of the iterated logarithm. Ann. Probab., 28:1870-1883．
[8] Kesten, H. (1965) , An iterated logarithm law for local time. Duke Math. J. , 32:447-456．
[9] Komlos,J., Major,P. and Tusady,G. (1975) , An approximation of partial sums of in-dependent R.V.'s and the sample DF.I. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 32:111-131．
[10] Komlos,J., Major,P. and Tusady,G. (1976) , An approximation of partial sums of in-dependent R.V.'s and the sample DF.II. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 34:33-58．
[11] Major,P.(1976) , The approximation of partial sums of independent r.v.'s. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 35:213-220．
[12] Revesz, P. (1990) , Random Walk in Random and Non-random Environments. Singa-pore: World Scientific.
[13] Zhang, L. X. (1998) , The United Form of the Strong Invariance and the Complete Convergence. Acta Math. Sinica (A), 41 (6) :1197-1210．
[14] Zhang, L. X. (2001a), The strong approximation for general Kesten-Spitzer random walk. Science in China (Series A), 44(5) :619-630．
[15] Zhang, L. X. (2001b), Precise asymptotics in the law of the iterated logarithm. Preprint.
[16] Zhang, L. X. (2001c), Precise rates in the Chung law of the iterated logarithm. Preprint.
[17] Zwillinger, D.(1996) , CRC Standard Mathematical Tables and Formulae. 30th Eds. CRC, Press, Inc.
[2] Csaki, E. (1989) , An integral test for the supremum of Wiener local time. Probab. Th. Rel. Fields, 83:207-217．
[3] Csaki, E. and Foldes, A. (1986) , How small are the increments of the local time of a Wiener process? Ann. Probab., 14:533-546．
[4] Csaki, E.,Csorgo, M., Foldes, A. and Revesz, P. (1983) , How big are the increments of the local time of a Wiener process? Ann. Probab., 11:593-608．
[5] Einmahl, U. (1989) , The Darling-Erdos theorem for sums of i.i.d. random variables. Probab. Theory Relat. Fields, 82: 241-257．
[6] Feller, W. (1945) , The law of the iterated logarithm for identically distributed random variables. Ann. Math., 47: 631-638．
[7] Gut, A. and Spataru, A. (2000) , Precise asymptotics in the law of the iterated logarithm. Ann. Probab., 28:1870-1883．
[8] Kesten, H. (1965) , An iterated logarithm law for local time. Duke Math. J. , 32:447-456．
[9] Komlos,J., Major,P. and Tusady,G. (1975) , An approximation of partial sums of in-dependent R.V.'s and the sample DF.I. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 32:111-131．
[10] Komlos,J., Major,P. and Tusady,G. (1976) , An approximation of partial sums of in-dependent R.V.'s and the sample DF.II. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 34:33-58．
[11] Major,P.(1976) , The approximation of partial sums of independent r.v.'s. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 35:213-220．
[12] Revesz, P. (1990) , Random Walk in Random and Non-random Environments. Singa-pore: World Scientific.
[13] Zhang, L. X. (1998) , The United Form of the Strong Invariance and the Complete Convergence. Acta Math. Sinica (A), 41 (6) :1197-1210．
[14] Zhang, L. X. (2001a), The strong approximation for general Kesten-Spitzer random walk. Science in China (Series A), 44(5) :619-630．
[15] Zhang, L. X. (2001b), Precise asymptotics in the law of the iterated logarithm. Preprint.
[16] Zhang, L. X. (2001c), Precise rates in the Chung law of the iterated logarithm. Preprint.
[17] Zwillinger, D.(1996) , CRC Standard Mathematical Tables and Formulae. 30th Eds. CRC, Press, Inc.