Mansuy, Roger; Yor, Marc Harnesses, Lévy bridges and Monsieur Jourdain. (English) Zbl 1070.60041 Stochastic Processes Appl. 115, No. 2, 329-338 (2005). Summary: Relations between harnesses and initial enlargements of the filtration of a Lévy process with its positions at fixed times are investigated. Cited in 19 Documents MSC: 60G51 Processes with independent increments; Lévy processes 60G48 Generalizations of martingales 60G44 Martingales with continuous parameter 60G10 Stationary stochastic processes Keywords:Lévy processes; Past-future martingales; Enlargement of filtration PDFBibTeX XMLCite \textit{R. Mansuy} and \textit{M. Yor}, Stochastic Processes Appl. 115, No. 2, 329--338 (2005; Zbl 1070.60041) Full Text: DOI arXiv References: [1] Borovkov, K.; Burq, Z., Kendall’s identity for the first crossing time revisited, Electron. Comm. Probab., 6, 91-94 (2001), (electronic) · Zbl 1008.60065 [2] L. Chaumont, M. Yor, Exercises in Probability, A Guided Tour from Measure Theory to Random Processes, via Conditioning, Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, Cambridge, 2003.; L. Chaumont, M. Yor, Exercises in Probability, A Guided Tour from Measure Theory to Random Processes, via Conditioning, Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, Cambridge, 2003. · Zbl 1065.60001 [3] G. Di Nunno, T. Meyer-Brandis, B. Øksendal, F. Proske, Optimal portfolio for an insider in a market driven by Lévy processes, submitted for publication, 2004.; G. Di Nunno, T. Meyer-Brandis, B. Øksendal, F. Proske, Optimal portfolio for an insider in a market driven by Lévy processes, submitted for publication, 2004. · Zbl 1136.91426 [4] Dozzi, M., Two-parameter harnesses and the Wiener process, Z. Wahrsch. Verw. Gebiete, 56, 4, 507-514 (1981) · Zbl 0456.60047 [5] M. Emery, M. Yor, A parallel between brownian bridges and gamma bridges, Publ. RIMS, Kyoto Univ., Vol. 40, No. 3, 2004, pp. 669-688.; M. Emery, M. Yor, A parallel between brownian bridges and gamma bridges, Publ. RIMS, Kyoto Univ., Vol. 40, No. 3, 2004, pp. 669-688. · Zbl 1074.60054 [6] P.A. Ferrari, L.R.G. Fontes, B.M. Niederhauser, M. Vachkovskaia, The serial harness interacting with a wall, arXiv:math.PR/0210218.; P.A. Ferrari, L.R.G. Fontes, B.M. Niederhauser, M. Vachkovskaia, The serial harness interacting with a wall, arXiv:math.PR/0210218. · Zbl 1070.60085 [7] P.A. Ferrari, B.M. Niederhauser, Harness processes and harmonic crystals, arXiv:math.PR/0312402.; P.A. Ferrari, B.M. Niederhauser, Harness processes and harmonic crystals, arXiv:math.PR/0312402. · Zbl 1111.60072 [8] P. Fitzsimmons, J. Pitman, M. Yor, Markovian bridges: construction, palm interpretation, and splicing, in: Seminar on Stochastic Processes, Seattle, WA, Progress in Probability, vol. 33, Birkhäuser, Boston, MA, 1993, pp. 101-134.; P. Fitzsimmons, J. Pitman, M. Yor, Markovian bridges: construction, palm interpretation, and splicing, in: Seminar on Stochastic Processes, Seattle, WA, Progress in Probability, vol. 33, Birkhäuser, Boston, MA, 1993, pp. 101-134. · Zbl 0844.60054 [9] J.M. Hammersley, Harnesses, in: Proceedings of the Fifth Berkeley Symposium Mathematical Statistics and Probability, Berkeley, CA, 1965/66, Physical Sciences, vol. III, University of California Press, Berkeley, CA, 1967, pp. 89-117.; J.M. Hammersley, Harnesses, in: Proceedings of the Fifth Berkeley Symposium Mathematical Statistics and Probability, Berkeley, CA, 1965/66, Physical Sciences, vol. III, University of California Press, Berkeley, CA, 1967, pp. 89-117. [10] Hammersley, J. M.; Mazzarino, G., Properties of large Eden clusters in the plane, Combin. Probab. Comput., 3, 4, 471-505 (1994) · Zbl 0834.60102 [11] K. Itô, Extension of stochastic integrals, in: Proceedings of the International Symposium on Stochastic Differential Equations, Research Institute Mathematical Science, Kyoto University, Kyoto, 1976, Wiley, New York, 1978, pp. 95-109.; K. Itô, Extension of stochastic integrals, in: Proceedings of the International Symposium on Stochastic Differential Equations, Research Institute Mathematical Science, Kyoto University, Kyoto, 1976, Wiley, New York, 1978, pp. 95-109. [12] Jacod, J.; Protter, P., Time reversal on Lévy processes, Ann. Probab., 16, 2, 620-641 (1988) · Zbl 0646.60052 [13] T. Jeulin, M. Yor, Inégalité de Hardy, semimartingales, et faux-amis, in: Séminaire de Probabilités, XIII Univ. Strasbourg, Strasbourg, 1977/78, Lecture Notes in Mathematics, vol. 721, Springer, Berlin, 1979, pp. 332-359.; T. Jeulin, M. Yor, Inégalité de Hardy, semimartingales, et faux-amis, in: Séminaire de Probabilités, XIII Univ. Strasbourg, Strasbourg, 1977/78, Lecture Notes in Mathematics, vol. 721, Springer, Berlin, 1979, pp. 332-359. [14] A. Kohatsu-Higa, M. Yamazoto, Enlargement of filtrations with random times for processes with jumps, Technical Report, 2004.; A. Kohatsu-Higa, M. Yamazoto, Enlargement of filtrations with random times for processes with jumps, Technical Report, 2004. [15] J.F.C. Kingman, The construction of infinite collections of random variables with linear regressions, Adv. Appl. Probab. (Suppl.) (1986) 73-85.; J.F.C. Kingman, The construction of infinite collections of random variables with linear regressions, Adv. Appl. Probab. (Suppl.) (1986) 73-85. · Zbl 0616.60005 [16] Lévy, P., Un théorème d’invariance projective relatif au mouvement brownien, Comment. Math. Helv., 16, 242-248 (1944) · Zbl 0063.03528 [17] Lévy, P., Une propriété d’invariance projective dans le mouvement brownien, C. R. Acad. Sci. Paris, 219, 378-379 (1944) · Zbl 0063.03529 [18] P.-A. Meyer, Sur une transformation du mouvement brownien due à Jeulin et Yor, in: Séminaire de Probabilités, XXVIII, Lecture Notes in Mathematics, vol. 1583, Springer, Berlin, 1994, pp. 98-101.; P.-A. Meyer, Sur une transformation du mouvement brownien due à Jeulin et Yor, in: Séminaire de Probabilités, XXVIII, Lecture Notes in Mathematics, vol. 1583, Springer, Berlin, 1994, pp. 98-101. · Zbl 0811.60064 [19] J.-B. Poquelin (known as Molière), Le bourgeois gentilhomme, 1670 Available form: \( \langle;\) http://gallica.bnf.fr/scripts/ConsultationTout.exe?\( \operatorname{O} = \operatorname{N} 023453\rangle;\); J.-B. Poquelin (known as Molière), Le bourgeois gentilhomme, 1670 Available form: \( \langle;\) http://gallica.bnf.fr/scripts/ConsultationTout.exe?\( \operatorname{O} = \operatorname{N} 023453\rangle;\) [20] P. Protter, Stochastic integration and differential equations, Applications of Mathematics (New York), second ed., vol. 21, Springer, Berlin, 2003.; P. Protter, Stochastic integration and differential equations, Applications of Mathematics (New York), second ed., vol. 21, Springer, Berlin, 2003. [21] Ken-iti Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge Studies in Advanced Mathematics, vol. 68, Cambridge University Press, Cambridge, 1999 (trans. from the 1990 Japanese original, revised by the author).; Ken-iti Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge Studies in Advanced Mathematics, vol. 68, Cambridge University Press, Cambridge, 1999 (trans. from the 1990 Japanese original, revised by the author). [22] Toom, A., Tails in harnesses, J. Statist. Phys., 88, 1-2, 347-364 (1997) · Zbl 0939.82013 [23] D. Williams, Some basic theorems on harnesses, in: Stochastic Analysis (a tribute to the memory of Rollo Davidson), Wiley, London, 1973, pp. 349-363.; D. Williams, Some basic theorems on harnesses, in: Stochastic Analysis (a tribute to the memory of Rollo Davidson), Wiley, London, 1973, pp. 349-363. [24] D. Williams, Brownian motion as a harness, University of Swansea, unpublished, 1980.; D. Williams, Brownian motion as a harness, University of Swansea, unpublished, 1980. [25] Zhou, Zhan Gong, Two-parameter harnesses and the generalized Brownian sheet, Natur. Sci. J. Xiangtan Univ., 14, 2, 111-115 (1992) · Zbl 0760.60052 [26] Zhuang, Xing Wu, The generalized Brownian sheet and two-parameter harnesses, Fujian Shifan Daxue Xuebao Ziran Kexue Ban, 4, 4, 1-9 (1988) [27] Run Chu Zhang, Xing Wu Zhuang, Two-parameter harnesses and a characterization of Brownian sheets, Kexue Tongbao 33 (22) (1988) 1694-1697 (in Chinese).; Run Chu Zhang, Xing Wu Zhuang, Two-parameter harnesses and a characterization of Brownian sheets, Kexue Tongbao 33 (22) (1988) 1694-1697 (in Chinese). · Zbl 1382.60108 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.