A non-skorohod topology on the skorohod space

Electronic Journal of Probability

Volumn 2, Issue , 1997, Pages 1-21

  Jakubowski, Adam ^a  

^a NICOLAUS COPERNICUS UNIVERSITY   (Poland)

Author keywords

Convergence in distribution; Semimartingales; Sequential spaces; Skorohod representation; Skorohod space

Indexed keywords

EID: 3042567006     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v2-18     Document Type: Article

References (20)

1. Dellacherie, C., Meyer, P.A. (1980) Probabilites et potentiel, Chapters V-VIII, Hermann, Paris 1980.
2. Engelking, R., General Topology, Helderman, Berlin 1989.
3. Fernique, X., Processus lineaires, processus generalises, Ann. Inst. Fourier (Grenoble), 17 (1967), 1-92.
4. Fernique, X., Convergence en loi de variables aletoires et de fonctions aletoires, proprietes de compacite des lois, II, in: J. Azema, P.A. Meyer, M. Yor, (Eds.) Séminaire de Probabilites XXVII, Lecture Notes in Math., 1557, 216-232, Springer, Berlin 1993.
5. Jakubowski, A., The a.s. Skorohod representation for subsequences in nonmetric spaces, Theory Probab. Appl., 42 (1997), 209-216.
6. Jakubowski, A., Convergence in various topologies for stochastic integrals driven by semimartingales, Ann. Probab., 24 (1996), 2141-2153.
7. Jakubowski, A., From convergence of functions to convergence of stochastic processes. On Skorokhod’s sequential approach to convergence in distribution., to appear in A Volume in Honour of A.V. Skorokhod, VSP, 1997.
8. 1de Skorokhod, Probab. Th. Rel. Fields, 81 (1989), 111-137.
9. Kantorowich, L.V., Vulih, B.Z. & Pinsker, A.G., Functional Analysis in Partially Ordered Spaces (in Russian), Gostekhizdat, Moscow 1950.
10. Kisynski, J., Convergence du type L, Colloq. Math., 7 (1960), 205-211.
11. Kurtz, T., Random time changes and convergence in distribution under the Meyer-Zheng conditions, Ann. Probab., 19 (1991), 1010-1034.
12. Kurtz, T., Protter, P., Weak limit theorems for stochastic integrals and stochastic differential equations, Ann. Probab., 19 (1991), 1035-1070.
13. Memin, J., Slomiňski, L. Condition UT et stabilite en loi des solutions d’equations differentieles stochastiques, Sém. de Probab. XXV, Lecture Notes in Math., 1485, 162-177, Springer, Berlin 1991.
14. Meyer, P.A., Zheng, W.A., Tightness criteria for laws of semimartingales, Ann. Inst. Henri Poincaré B, 20 (1984), 353-372.
15. Protter, Ph., Stochastic Integration and Differential Equations. A New Approach., 2nd Ed., Springer 1992.
16. Skorohod, A.V., Limit theorems for stochastic processes, Theor. Probability Appl., 1 (1956), 261-290.
17. Slomiňski, L., Stability of strong solutions of stochastic differential equations, Stoch. Proc. Appl., 31 (1989), 173-202.
18. Slomiňski, L., Stability of stochastic differential equations driven by general semimartingales, Dissertationes Math., Vol CCCXLIX (1996), 113 p.
19. Stricker, C., Lois de semimartingales et criteres de compacite, Séminares de probabilités XIX. Lect. Notes in Math., 1123, Springer, Berlin 1985.
20. Topsoe, F., A criterion for weak convergence of measures with an application to convergence of measures on ID [0,1], Math. Scand., 25 (1969), 97-104