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@article{DMDICO_2009_29_1_a5, author = {Michta, Mariusz}, title = {Weak solutions of stochastic differential inclusions and their compactness}, journal = {Discussiones Mathematicae. Differential Inclusions, Control and Optimization}, pages = {91--106}, publisher = {mathdoc}, volume = {29}, number = {1}, year = {2009}, zbl = {1206.93107}, language = {en}, url = {http://geodesic.mathdoc.fr/item/DMDICO_2009_29_1_a5/} }
TY - JOUR AU - Michta, Mariusz TI - Weak solutions of stochastic differential inclusions and their compactness JO - Discussiones Mathematicae. Differential Inclusions, Control and Optimization PY - 2009 SP - 91 EP - 106 VL - 29 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMDICO_2009_29_1_a5/ LA - en ID - DMDICO_2009_29_1_a5 ER -
%0 Journal Article %A Michta, Mariusz %T Weak solutions of stochastic differential inclusions and their compactness %J Discussiones Mathematicae. Differential Inclusions, Control and Optimization %D 2009 %P 91-106 %V 29 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/DMDICO_2009_29_1_a5/ %G en %F DMDICO_2009_29_1_a5
Michta, Mariusz. Weak solutions of stochastic differential inclusions and their compactness. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 29 (2009) no. 1, pp. 91-106. http://geodesic.mathdoc.fr/item/DMDICO_2009_29_1_a5/
[1] N.U. Ahmed, Nonlinear stochastic differential inclusions on Banach space, Stoch. Anal. Appl. 12 (1) (1994), 1-10.
[2] N.U. Ahmed, Impulsive perturbation of C₀ semigroups and stochastic evolution inclusions, Discuss. Math. DICO 22 (1) (2002), 125-149.
[3] N.U. Ahmed, Optimal relaxed controls for nonlinear infinite dimensional stochastic differential inclusions, Optimal Control of Differential Equations, M. Dekker Lect. Notes. 160 (1994), 1-19.
[4] N.U. Ahmed, Optimal relaxed controls for infinite dimensional stochastic systems of Zakai type, SIAM J. Contr. Optim. 34 (5) (1996), 1592-1615.
[5] P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968.
[6] S. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Vol. 1, Theory, Kluwer, Boston, 1997.
[7] J. Jacod, Weak and strong solutions of stochastic differential equations, Stochastics 3 (1980), 171-191.
[8] J. Jacod, A.N. Shiryaev, Limit Theorems for Stochastic Processes. Springer, New York, 1987.
[9] M. Kisielewicz, M. Michta, J. Motyl, Set-valued approach to stochastic control. Parts I, II, Dynamic. Syst. Appl. 12 (34) (2003), 405-466.
[10] M. Kisielewicz, Quasi-retractive representation of solution set to stochastic inclusions, J. Appl. Math. Stochastic Anal. 10 (3) (1997), 227-238.
[11] M. Kisielewicz, Set-valued stochastic integrals and stochastic inclusions, Stoch. Anal. Appl. 15 (5) (1997), 783-800.
[12] M. Kisielewicz, Stochastic differential inclusions, Discuss. Math. Differential Incl. 17 (1-2) (1997), 51-65.
[13] M. Kisielewicz, Weak compactness of solution sets to stochastic differential inclusions with convex right-hand side, Topol. Meth. Nonlin. Anal. 18 (2003), 149-169.
[14] M. Kisielewicz, Weak compactness of solution sets to stochastic differential inclusions with non-convex right-hand sides, Stoch. Anal. Appl. 23 (5) (2005), 871-901.
[15] M. Kisielewicz, Stochastic differential inclusions and diffusion processes, J. Math. Anal. Appl. 334 (2) (2007), 1039-1054.
[16] A.A. Levakov, Stochastic differential inclusions, J. Differ. Eq. 2 (33) (2003), 212-221.
[17] M. Michta, On weak solutions to stochastic differential inclusions driven by semimartingales, Stoch. Anal. Appl. 22 (5) (2004), 1341-1361.
[18] M. Michta, Optimal solutions to stochastic differential inclusions, Applicationes Math. 29 (4) (2002), 387-398.
[19] M. Michta and J. Motyl, High order stochastic inclusions and their applications, Stoch. Anal. Appl. 23 (2005), 401-420.
[20] J. Motyl, Stochastic functional inclusion driven by semimartingale, Stoch. Anal. Appl. 16 (3) (1998), 517-532.
[21] J. Motyl, Existence of solutions of set-valued Itô equation, Bull. Acad. Pol. Sci. 46 (1998), 419-430.
[22] P. Protter, Stochastic Integration and Differential Equations: A New Approach, Springer, New York, 1990.
[23] L. Słomiński, Stability of stochastic differential equations driven by general semimartingales, Dissertationes Math. 349 (1996), 1-109.
[24] C. Stricker, Loi de semimartingales et critéres de compacité, Sem. de Probab. XIX Lecture Notes in Math. 1123 (1985), Springer Berlin.
[25] D. Stroock and S.R. Varadhan, Multidimensional Diffusion Processes, Springer, 1975.