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Volumn 117, Issue 10, 2007, Pages 1540-1560

The estimates of the mean first exit time from a ball for the α-stable Ornstein-Uhlenbeck processes

Author keywords

stable process; Exit time; Ornstein Uhlenbeck process

Indexed keywords

DIFFUSION; STATISTICAL METHODS;

EID: 34548204479     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2007.02.007     Document Type: Article
Times cited : (13)

References (19)
  • 1
    • 33644971385 scopus 로고    scopus 로고
    • Representations of the first hitting time density of an Ornstein-Uhlenbeck process
    • Alili L., Patie P., and Pedersen J.L. Representations of the first hitting time density of an Ornstein-Uhlenbeck process. Stoch. Models 21 4 (2005) 967-980
    • (2005) Stoch. Models , vol.21 , Issue.4 , pp. 967-980
    • Alili, L.1    Patie, P.2    Pedersen, J.L.3
  • 2
    • 16744365634 scopus 로고    scopus 로고
    • Symmetric stable processes in cones
    • Bañuelos R., and Bogdan K. Symmetric stable processes in cones. Potential Anal. 21 3 (2004) 263-288
    • (2004) Potential Anal. , vol.21 , Issue.3 , pp. 263-288
    • Bañuelos, R.1    Bogdan, K.2
  • 3
    • 0142137750 scopus 로고    scopus 로고
    • Harnack inequality for stable processes on d-sets
    • Bogdan K., Stós A., and Sztonyk P. Harnack inequality for stable processes on d-sets. Studia Math. 158 2 (2003) 163-198
    • (2003) Studia Math. , vol.158 , Issue.2 , pp. 163-198
    • Bogdan, K.1    Stós, A.2    Sztonyk, P.3
  • 4
    • 0037253515 scopus 로고    scopus 로고
    • Stable processes have thorns
    • Burdzy K., and Kulczycki T. Stable processes have thorns. Ann. Probab. 31 1 (2003) 170-194
    • (2003) Ann. Probab. , vol.31 , Issue.1 , pp. 170-194
    • Burdzy, K.1    Kulczycki, T.2
  • 5
    • 0039679171 scopus 로고
    • Conditional transformation of drift formula and potential theory for frac(1, 2) Δ + b ({dot operator}) {dot operator} ∇
    • Cranston M., and Zhao Z. Conditional transformation of drift formula and potential theory for frac(1, 2) Δ + b ({dot operator}) {dot operator} ∇. Comm. Math. Phys. 112 4 (1987) 613-625
    • (1987) Comm. Math. Phys. , vol.112 , Issue.4 , pp. 613-625
    • Cranston, M.1    Zhao, Z.2
  • 6
    • 0034345360 scopus 로고    scopus 로고
    • Ornstein-Uhlenbeck-Cauchy process
    • Garbaczewski P., and Olkiewicz R. Ornstein-Uhlenbeck-Cauchy process. J. Math. Phys. 41 10 (2000) 6843-6860
    • (2000) J. Math. Phys. , vol.41 , Issue.10 , pp. 6843-6860
    • Garbaczewski, P.1    Olkiewicz, R.2
  • 7
    • 0007322689 scopus 로고
    • First passage times for symmetric stable processes in space
    • Getoor R.K. First passage times for symmetric stable processes in space. Trans. Amer. Math. Soc. 101 (1961) 75-90
    • (1961) Trans. Amer. Math. Soc. , vol.101 , pp. 75-90
    • Getoor, R.K.1
  • 8
    • 1042285606 scopus 로고    scopus 로고
    • A survey and some generalizations of Bessel processes
    • Göing-Jaeschke A., and Yor M. A survey and some generalizations of Bessel processes. Bernoulli 9 2 (2003) 313-349
    • (2003) Bernoulli , vol.9 , Issue.2 , pp. 313-349
    • Göing-Jaeschke, A.1    Yor, M.2
  • 9
    • 34548204475 scopus 로고    scopus 로고
    • P. Graczyk, T. Jakubowski, Exit times and Poisson kernels of the Ornstein-Uhlenbeck process, 2005, Preprint
  • 10
    • 0037401191 scopus 로고    scopus 로고
    • Tails of solutions of certain nonlinear stochastic differential equations driven by heavy tailed Lévy motions
    • Grigoriu M., and Samorodnitsky G. Tails of solutions of certain nonlinear stochastic differential equations driven by heavy tailed Lévy motions. Stochastic Process. Appl. 105 1 (2003) 69-97
    • (2003) Stochastic Process. Appl. , vol.105 , Issue.1 , pp. 69-97
    • Grigoriu, M.1    Samorodnitsky, G.2
  • 11
    • 32844462489 scopus 로고    scopus 로고
    • First exit times of SDEs driven by stable Lévy processes
    • Imkeller P., and Pavlyukevich I. First exit times of SDEs driven by stable Lévy processes. Stochastic Process. Appl. 116 4 (2006) 69-97
    • (2006) Stochastic Process. Appl. , vol.116 , Issue.4 , pp. 69-97
    • Imkeller, P.1    Pavlyukevich, I.2
  • 13
    • 10844238417 scopus 로고    scopus 로고
    • Martingales and first-exit times for the Ornstein-Uhlenbeck process with jumps
    • Novikov A.A. Martingales and first-exit times for the Ornstein-Uhlenbeck process with jumps. Teor. Veroyatn. Primen. 48 2 (2003) 340-358
    • (2003) Teor. Veroyatn. Primen. , vol.48 , Issue.2 , pp. 340-358
    • Novikov, A.A.1
  • 14
    • 14844345068 scopus 로고    scopus 로고
    • On a martingale associated to generalized Ornstein-Uhlenbeck processes and an application to finance
    • Patie P. On a martingale associated to generalized Ornstein-Uhlenbeck processes and an application to finance. Stochastic Process. Appl. 15 4 (2005) 593-607
    • (2005) Stochastic Process. Appl. , vol.15 , Issue.4 , pp. 593-607
    • Patie, P.1
  • 15
    • 33646590061 scopus 로고    scopus 로고
    • Springer-Verlag, Berlin
    • Protter P.E. Stochastic Integration and Differential Equations: Stochastic Modelling and Applied Probability. second ed. Applications of Mathematics (New York) vol. 21 (2004), Springer-Verlag, Berlin
    • (2004) Applications of Mathematics (New York) , vol.21
    • Protter, P.E.1
  • 16
    • 0000711915 scopus 로고
    • First-passage-time density and moments of the Ornstein-Uhlenbeck process
    • Ricciardi L.M., and Sato S. First-passage-time density and moments of the Ornstein-Uhlenbeck process. J. Appl. Probab. 25 1 (1988) 43-57
    • (1988) J. Appl. Probab. , vol.25 , Issue.1 , pp. 43-57
    • Ricciardi, L.M.1    Sato, S.2
  • 17
    • 0039986371 scopus 로고
    • Chapman & Hall, New York
    • Samorodnitsky G., and Taqqu M.S. Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. Stochastic Modeling (1994), Chapman & Hall, New York
    • (1994) Stochastic Modeling
    • Samorodnitsky, G.1    Taqqu, M.S.2
  • 18
    • 0000031273 scopus 로고
    • Evaluation of the first-passage time probability to a square root boundary for the Wiener process
    • Sato S. Evaluation of the first-passage time probability to a square root boundary for the Wiener process. J. Appl. Probab. 14 4 (1977) 850-856
    • (1977) J. Appl. Probab. , vol.14 , Issue.4 , pp. 850-856
    • Sato, S.1
  • 19
    • 0016555338 scopus 로고
    • Some mean first-passage time approximations for the Ornstein-Uhlenbeck process
    • Thomas M.U. Some mean first-passage time approximations for the Ornstein-Uhlenbeck process. J. Appl. Probab. 12 3 (1975) 600-604
    • (1975) J. Appl. Probab. , vol.12 , Issue.3 , pp. 600-604
    • Thomas, M.U.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.