×

zbMATH — the first resource for mathematics

Continuity of local times for Markov processes. (English) Zbl 0293.60069

MSC:
60J55 Local time and additive functionals
60J99 Markov processes
60J25 Continuous-time Markov processes on general state spaces
60G17 Sample path properties
PDF BibTeX XML Cite
Full Text: Numdam EuDML
References:
[1] S.M. Berman [1] Gaussian processes with stationary increments: local times and sample function properties , Ann. Math. Stat. 41 (1970) 1260-1272. · Zbl 0204.50501 · doi:10.1214/aoms/1177696901
[2] R.M. Blumenthal And R.K. Getoor [2] Local times for Markov processes , Z. Wahrscheinlichkeitstheorie verw. Geb. 3 (1964) 50-74. · Zbl 0126.33701 · doi:10.1007/BF00531683
[3] R.M. Blumenthal And R.K. Getoor [3] Markov processes and potential theory , Academic Press, New York, 1968. · Zbl 0169.49204 · www.sciencedirect.com
[4] E.S. Boylan [4] Local times for a class of Markov processes , Ill. J. Math. 8 (1964) 19-39. · Zbl 0126.33702
[5] L. Breiman [5] Probability , Addison-Wesley Publ. Co., Reading, Mass., 1968. · Zbl 0174.48801
[6] J. Bretagnolle [6 ] Résultats de Kesten sur les processus à accroissements indépendants . Lecture Notes in Mathematics, Vol. 191, Springer-Verlag, Berlin (1971) 21-36. · www.numdam.org
[7] K.L. Chung [7] A course in probability theory , Harcourt, Brace & World, Inc. New York, 1968. · Zbl 0159.45701
[8] L.E. Dubins And D.A. Freedman [8] A sharper form of the Borel-Cantelli lemma and the strong law , Ann. Math. Stat. 36 (1965) 800-807. · Zbl 0168.16901 · doi:10.1214/aoms/1177700054
[9] A.M. Garsia , E. Rodemich AND H. Rumsey, Jr. [9] A real variable lemma and the continuity of paths of some Gaussian processes , Indiana Univ. Math J. 20 (1970) 565-578. · Zbl 0252.60020 · doi:10.1512/iumj.1970.20.20046
[10] A.M. Garsia [10] Continuity properties of multi-dimensional Gaussian processes , 6th Berkeley Symposium on Math. Stat. and Prob., p. 000, Berkeley 1970. · Zbl 0272.60034
[11] R.K. Getoor [11] Continuous additive functionals of a Markov process with applications to processes with independent increments , J. Math. Anal. Appl. 13 (1966) 132-153. · Zbl 0138.40901 · doi:10.1016/0022-247X(66)90079-5
[12] K. Ito And H.P. Mckean, Jr. [12] Diffusion processes and their sample paths , Springer-Verlag, Berlin, 1965. · Zbl 0127.09503
[13] H. Kesten [13] Hitting probabilities of single points for processes with stationary independent increments, Memoir 93 , Am. Math. Soc., 1969. · Zbl 0186.50202
[14] P.A. Meyer [14] Sur les lois de certaines functionelles additives; Applications aux temps locaux , Publ. Inst. Stat. Univ. Paris 15 (1966) 295-310. · Zbl 0144.40102
[15] P.A. Meyer [15] Processus de Markov , Lecture Notes in Mathematics, vol. 26, Springer-Verlag, Berlin, 1967. · Zbl 0189.51403 · doi:10.1007/BFb0075148
[16] S.C. Port And C.J. Stone [16] The asymmetric Cauchy processes on the line , Ann. Math. Stat. 40 (1969) 137-143. · Zbl 0211.21102 · doi:10.1214/aoms/1177697810
[17] S.C. Port And C.J. Stone [17] Infinitely divisible processes and their potential theory , Ann. Inst. Fourier 21 (1971) 157-257. · Zbl 0195.47601 · doi:10.5802/aif.376 · numdam:AIF_1971__21_2_157_0 · numdam:AIF_1971__21_4_179_0 · eudml:74032
[18] C. Stone [18] The set of zeros of a semistable process , Ill. J. Math. 7 (1963) 631-637. · Zbl 0121.12906
[19] H.F. Trotter [19] A property of Brownian motion paths , Ill. J. Math. 2 (1958) 425-433. · Zbl 0117.35502
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.