메뉴 건너뛰기




Volumn 14, Issue 4, 2008, Pages 963-987

Convergence of excursion point processes and its applications to functional limit theorems of Markov processes on a half-line

Author keywords

Feller's boundary condition; Functional limit theorems; Invariance principles; It 's excursion theory

Indexed keywords


EID: 58149328723     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/08-BEJ132     Document Type: Article
Times cited : (10)

References (25)
  • 1
    • 58149332916 scopus 로고    scopus 로고
    • Bingham, N.H., Goldie, C.M. and Teugels, J.L. (1989). Regular Variation. Encyclopedia of Mathematics and Its Applications 27. Cambridge: Cambridge Univ. Press. MR1015093
    • Bingham, N.H., Goldie, C.M. and Teugels, J.L. (1989). Regular Variation. Encyclopedia of Mathematics and Its Applications 27. Cambridge: Cambridge Univ. Press. MR1015093
  • 2
    • 58149343018 scopus 로고    scopus 로고
    • Blumenthal, R.M. (1992). Excursions of Markov Processes. Probability and Its Applications. Boston, MA: Birkhäuser. MR1138461
    • Blumenthal, R.M. (1992). Excursions of Markov Processes. Probability and Its Applications. Boston, MA: Birkhäuser. MR1138461
  • 3
    • 58149349483 scopus 로고
    • A martingale approach to the Poisson convergence of simple point processes
    • MR0482991
    • Brown, T. (1978). A martingale approach to the Poisson convergence of simple point processes. Ann. Probab. 6 615-628. MR0482991
    • (1978) Ann. Probab , vol.6 , pp. 615-628
    • Brown, T.1
  • 4
    • 0000918549 scopus 로고
    • Functional limit theorems for dependent variables
    • MR0503954
    • Durrett, R. and Resnick, S.I. (1978). Functional limit theorems for dependent variables. Ann. Probab. 6 829-846. MR0503954
    • (1978) Ann. Probab , vol.6 , pp. 829-846
    • Durrett, R.1    Resnick, S.I.2
  • 5
    • 0001254093 scopus 로고
    • The parabolic differential equations and the associated semi-groups of transformations
    • MR0047886
    • Feller, W. (1952). The parabolic differential equations and the associated semi-groups of transformations. Ann. of Math. (2) 55 468-519. MR0047886
    • (1952) Ann. of Math. (2) , vol.55 , pp. 468-519
    • Feller, W.1
  • 6
    • 38349123869 scopus 로고    scopus 로고
    • Time change approach to generalized excursion measures, and its application to limit theorems
    • MR2384481
    • Fitzsimmons, P.J. and Yano, K. (2008). Time change approach to generalized excursion measures, and its application to limit theorems. J. Theoret. Probab. 21 246-265. MR2384481
    • (2008) J. Theoret. Probab , vol.21 , pp. 246-265
    • Fitzsimmons, P.J.1    Yano, K.2
  • 7
    • 58149344714 scopus 로고    scopus 로고
    • Itô, K. (1972). Poisson point processes attached to Markov processes. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability III (Univ. California, Berkeley, Calif., 1970/1971). Probability Theory 225-239. Berkeley, CA: Univ. California Press. MR0402949
    • Itô, K. (1972). Poisson point processes attached to Markov processes. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability III (Univ. California, Berkeley, Calif., 1970/1971). Probability Theory 225-239. Berkeley, CA: Univ. California Press. MR0402949
  • 8
    • 58149345253 scopus 로고
    • Poisson point processes and their application to Markov processes. Lecture note of Mathematics Department, Kyoto Univ
    • unpublished
    • Itô, K. (1969). Poisson point processes and their application to Markov processes. Lecture note of Mathematics Department, Kyoto Univ., unpublished.
    • (1969)
    • Itô, K.1
  • 9
    • 84972526382 scopus 로고
    • Brownian motions on a half line
    • MR0154338
    • Itô, K. and McKean, Jr, H.P. (1963). Brownian motions on a half line. Illinois J. Math. 7 181-231. MR0154338
    • (1963) Illinois J. Math , vol.7 , pp. 181-231
    • Itô, K.1    McKean Jr, H.P.2
  • 10
    • 58149345250 scopus 로고    scopus 로고
    • Jacod, J. (1985). Théorèmes limite pour les processus. École d'Éte de Probabilités de Saint-Flour XIII - 1983 298 - 409. Lecture Notes in Math. 1117. Berlin: Springer. MR0883648
    • Jacod, J. (1985). Théorèmes limite pour les processus. École d'Éte de Probabilités de Saint-Flour XIII - 1983 298 - 409. Lecture Notes in Math. 1117. Berlin: Springer. MR0883648
  • 11
    • 34250103054 scopus 로고
    • Sur la convergence des processus ponctuels.
    • MR0917680
    • Jacod, J. (1987). Sur la convergence des processus ponctuels. Probab. Theory Related Fields 76 573-586. MR0917680
    • (1987) Probab. Theory Related Fields , vol.76 , pp. 573-586
    • Jacod, J.1
  • 12
    • 58149351106 scopus 로고    scopus 로고
    • Jacod, J. and Shiryaev, A.N. (2003). Limit Theorems for Stochastic Processes, 2nd ed. Grundlehren der Mathematischen Wissenschaften 288. Berlin: Springer. MR1943877
    • Jacod, J. and Shiryaev, A.N. (2003). Limit Theorems for Stochastic Processes, 2nd ed. Grundlehren der Mathematischen Wissenschaften 288. Berlin: Springer. MR1943877
  • 13
    • 58149343014 scopus 로고    scopus 로고
    • Jeulin, T. (1980). Semi-Martingales et Grossissement d'une Filtration. Lecture Notes in Math. 833. Berlin: Springer. MR0604176
    • Jeulin, T. (1980). Semi-Martingales et Grossissement d'une Filtration. Lecture Notes in Math. 833. Berlin: Springer. MR0604176
  • 14
    • 0001442817 scopus 로고
    • Limit theorems for Lévy processes and Poisson point processes and their applications to Brownian excursions
    • MR0766640
    • Kasahara, Y. (1984). Limit theorems for Lévy processes and Poisson point processes and their applications to Brownian excursions. J. Math. Kyoto Univ. 24 521-538. MR0766640
    • (1984) J. Math. Kyoto Univ , vol.24 , pp. 521-538
    • Kasahara, Y.1
  • 15
    • 0347460742 scopus 로고    scopus 로고
    • Kasahara, Y. and Maejima, M. (1986). Functional limit theorems for weighted sums of i.i.d. random variables. Probab. Theory Related Fields 72 161-183. MR0836273
    • Kasahara, Y. and Maejima, M. (1986). Functional limit theorems for weighted sums of i.i.d. random variables. Probab. Theory Related Fields 72 161-183. MR0836273
  • 16
    • 84972494091 scopus 로고
    • Limit theorems for point processes and their functionals
    • MR0845720
    • Kasahara, Y and Watanabe, S. (1986). Limit theorems for point processes and their functionals. J. Math. Soc. Japan 38 543-574. MR0845720
    • (1986) J. Math. Soc. Japan , vol.38 , pp. 543-574
    • Kasahara, Y.1    Watanabe, S.2
  • 17
    • 33751028143 scopus 로고    scopus 로고
    • Brownian representation of a class of Lévy processes and its application to occupation times of diffusion processes
    • electronic, MR2247838
    • Kasahara, Y. and Watanabe, S. (2006). Brownian representation of a class of Lévy processes and its application to occupation times of diffusion processes. Illinois J. Math. 50 515-539 (electronic). MR2247838
    • (2006) Illinois J. Math , vol.50 , pp. 515-539
    • Kasahara, Y.1    Watanabe, S.2
  • 18
    • 34250470397 scopus 로고
    • Semi-stable Markov processes. I
    • MR0307358
    • Lamperti, J. (1972). Semi-stable Markov processes. I. Z. Wahrsch. Verw. Gebiete 22 205-225. MR0307358
    • (1972) Z. Wahrsch. Verw. Gebiete , vol.22 , pp. 205-225
    • Lamperti, J.1
  • 19
    • 1942475915 scopus 로고    scopus 로고
    • A conditional limit theorem for generalized diffusion processes
    • MR2028667
    • Li, Z., Shiga, T. and Tomisaki, M. (2003). A conditional limit theorem for generalized diffusion processes. J. Math. Kyoto Univ. 43 567-583. MR2028667
    • (2003) J. Math. Kyoto Univ , vol.43 , pp. 567-583
    • Li, Z.1    Shiga, T.2    Tomisaki, M.3
  • 20
    • 0001407755 scopus 로고
    • Weak convergence of probability measures and random functions in the function space D(0, ∞)
    • MR0362429
    • Lindvall, T. (1973). Weak convergence of probability measures and random functions in the function space D(0, ∞). J. Appl. Probab. 10 109-121. MR0362429
    • (1973) J. Appl. Probab , vol.10 , pp. 109-121
    • Lindvall, T.1
  • 21
    • 58149339357 scopus 로고    scopus 로고
    • Meyer, P.A. (1971). Processus de Poisson ponctuels, d'après K. Ito. Séminaire de Probabilités V (Univ. Strasbourg, année universitaire 1969-1970) 177-190. Lecture Notes in Math. 191. Berlin: Springer. MR0388551
    • Meyer, P.A. (1971). Processus de Poisson ponctuels, d'après K. Ito. Séminaire de Probabilités V (Univ. Strasbourg, année universitaire 1969-1970) 177-190. Lecture Notes in Math. 191. Berlin: Springer. MR0388551
  • 22
    • 58149343015 scopus 로고    scopus 로고
    • Pitman, J.W. and Yor, M. (1986). Some divergent integrals of Brownian motion. Adv. in Appl. Probab. suppl. 109-116. MR0868512
    • Pitman, J.W. and Yor, M. (1986). Some divergent integrals of Brownian motion. Adv. in Appl. Probab. suppl. 109-116. MR0868512
  • 23
    • 0001353916 scopus 로고
    • Limit theorems for random walks, birth and death processes, and diffusion processes
    • MR0158440
    • Stone, C. (1963). Limit theorems for random walks, birth and death processes, and diffusion processes. Illinois J. Math. 7 638-660. MR0158440
    • (1963) Illinois J. Math , vol.7 , pp. 638-660
    • Stone, C.1
  • 24
    • 58149334569 scopus 로고    scopus 로고
    • Watanabe, S. (1995). Generalized arc-sine laws for one-dimensional diffusion processes and random walks. In Stochastic Analysis (Ithaca, NY 1993). Proc. Sympos. Pure Math. 57 157-172. Providence, RI: Amer. Math. Soc. MR1335470
    • Watanabe, S. (1995). Generalized arc-sine laws for one-dimensional diffusion processes and random walks. In Stochastic Analysis (Ithaca, NY 1993). Proc. Sympos. Pure Math. 57 157-172. Providence, RI: Amer. Math. Soc. MR1335470
  • 25
    • 33751063174 scopus 로고    scopus 로고
    • Excursion measure away from an exit boundary of one-dimensional diffusion processes
    • MR2266999
    • Yano, K. (2006). Excursion measure away from an exit boundary of one-dimensional diffusion processes. Publ. RIMS 42 837-878. MR2266999
    • (2006) Publ. RIMS , vol.42 , pp. 837-878
    • Yano, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.