Statistical causality, extremal measures and weak solutions of stochastic differential equations with driving semimartingales

Journal of Mathematical Modelling and Algorithms

Volumn 9, Issue 1, 2010, Pages 113-128

  Petrović, Ljiljana ^a   Stanojević, Dragana ^b  

^a UNIVERSITY OF BELGRADE   (Serbia)

^b UNIVERSITY OF PRI TINA   (Serbia)

Author keywords

Causality; Extremal measure; Filtration; Martingale problem; Semimartingale; Stochastic differential equation; Weak solution; Weak uniqueness

Indexed keywords

EID: 76649098294     PISSN: 15701166     EISSN: 15729214     Source Type: Journal    
DOI: 10.1007/s10852-009-9121-5     Document Type: Article

References (21)

1. Bremaud, P., Yor, M.: Changes of filtration and of probability measures. Z. Wahrscheinlichkeitstheor. Verw. Geb. 45, 269-295 (1978).
2. Elliot, R. J.: Stochastic calculus and applications. Springer, New York (1982).
3. Gill, J. B., Petrović, L.: Causality and stochastic dynamic systems. SIAM J. Appl. Math. 47(6), 1361-1366 (1987).
4. Granger, C. W. J.: Investigating causal relations by econometric models and cross spectral methods. Econometrica 37, 424-438 (1969).
5. Jacod, J.: Calcul stochastique et problemes de martingales. Lecture Notes, Berlin (1979).
6. Jacod, J.: Weak and strong solutions of stochastic differential equations. Stochastics 3, 171-191 (1980).
7. Jacod, J., Shiryaev, A. N.: Limit theorems for stochastic processes (on Russian). Springer, Moskva (1994).
8. Jacod, J., Memin, J.: Existence of weak solutions for stochastic differential equation with driving semimartingales. Stochastics 4, 317-337 (1981).
9. Kallsen, J.: Semimartingale modelling and finance, doctoral dissertation. University of Freiburg (1998).
10. Lebedev, V. A.: on the existence of weak solutions for stochastic differential equations with driving martingales and random measures. Stochastics 9, 37-76 (1981).
11. Mykland, P. A.: Statistical causality. University of Bergen, Bergen (1986).
12. Mykland, P. A.: Stable subspaces over regular solutions of martingale problems. University of Bergen, Bergen (1986).
13. Petrović, L.: Causality and markovian reductions and extensions of a family of hilbert spaces. J. Math. Systems, Estimat. Control. 8(4), 12 (1998).
14. Petrović, L., Stanojević, D.: Some models of causality and weak solutions of stochastic differential equations with driving semimartingales. Facta Universitatis, (Niš), Ser. Math. Inform. 20(5), 103-112 (2005).
15. Royden, H. J.: Real analysis. Collier Macmillan, New York (1968).
16. Rozanov, Yu. A.: Theory of innovation processes, monographs in probability theory and mathematical statistics, Izdat. Nauka, Moscow (1974).
17. Rozanov, Yu. A.: Innovation processes. Winston, New York (1977).
18. Strook, D. V., Yor, M.: On extremal solutions of martingale problems. Am. Scient. Ecole Norm. Sup. 13, 95-164 (1980).
19. Strook, D. V., Varadhan, S.: Diffusion processeswith continuous coeffitients, I and II. Commun. Pure Appl. Math. XXII 345-400, 479-530 (1969).
20. Strook, D. V., Varadhan, S.: Multidimensional diffusion processes, reprint of 1997 edition. Springer, New York (2000).
21. Yor, M.: Sur L'Etude des martingales continues extremales. Stochastics 2, 191-196 (1979).