A Criterion for the Viability of Stochastic Semilinear Control Systems via the Quasi-Tangency Condition
作者： Dan Goreac
关键词: Applied mathematics 、 Property (philosophy) 、 Tangent 、 Separable hilbert space 、 Mathematical analysis 、 Linear control systems 、 Mathematics 、 Unit sphere 、 Control system
摘要: In this paper we study a criterion for the viability of stochastic semilinear control systems on real, separable Hilbert space. The necessary and sufficient conditions are given using notion quasi-tangency. As consequence, prove that approximate property coincide linear systems. We obtain Nagumo's theorem present method allowing to provide explicit criteria smooth sets. analyze characterizing unit ball. generalizes recent results from deterministic framework.
harvard.edu
arxiv.org
sci-hub.st 参考文章(13)
Ovidiu Cârja, Mihai Necula, Ioan I Vrabie, Viability, Invariance and Applications Elsevier Science. ,(2007)
Lionel Thibault, Serge Gautier, Viability for constrained stochastic differential equations Differential and Integral Equations. ,vol. 6, pp. 1395- 1414 ,(1993)
Giuseppe Da Prato, Jerzy Zabczyk, Stochastic Equations in Infinite Dimensions ,(1992)
Ovidiu Cârjă, Mihai Necula, Ioan I. Vrabie, Necessary and sufficient conditions for viability for semilinear differential inclusions Transactions of the American Mathematical Society. ,vol. 361, pp. 343- 390 ,(2008) , 10.1090/S0002-9947-08-04668-0
Rainer Buckdahn, Shige Peng, Marc Quincampoix, Catherine Rainer, Existence of stochastic control under state constraints Comptes Rendus de l'Académie des Sciences - Series I - Mathematics. ,vol. 327, pp. 17- 22 ,(1998) , 10.1016/S0764-4442(98)80096-7
Ioan I. Vrabie, Ovidiu Cârjă, Some new viability results for semilinear differential inclusions Nodea-nonlinear Differential Equations and Applications. ,vol. 4, pp. 401- 424 ,(1997) , 10.1007/S000300050022
Dan Goreac, Non-compact-valued stochastic control under state constraints Bulletin Des Sciences Mathematiques. ,vol. 131, pp. 716- 737 ,(2007) , 10.1016/J.BULSCI.2006.08.001
Rainer Buckdahn, Marc Quincampoix, Aurel Răşcanu, Viability property for a backward stochastic differential equation and applications to partial differential equations Probability Theory and Related Fields. ,vol. 116, pp. 485- 504 ,(2000) , 10.1007/S004400050260
R. Buckdahn, P. Cardaliaguet, M. Quincampoix, A Representation Formula for the Mean Curvature Motion Siam Journal on Mathematical Analysis. ,vol. 33, pp. 827- 846 ,(2001) , 10.1137/S0036141000380334
Rainer Buckdahn, Marc Quincampoix, Gianmario Tessitore, Controlled Stochastic Differential Equations under Constraints in Infinite Dimensional Spaces Siam Journal on Control and Optimization. ,vol. 47, pp. 218- 250 ,(2008) , 10.1137/060674284