Stochastic viability and invariance, Annali Scuola Normale di Pisa, issue.27, pp.595-694, 1990. ,
Viability theory, 1991. ,
URL : https://hal.archives-ouvertes.fr/inria-00636570
Set-valued analysis, Birkhäuser, 1990. ,
DOI : 10.1007/978-3-642-60756-1_11
Invariant sets for controlled degenerate diffusions: A viscosity solutions approach, Stochastic Analysis, Control, Optimization and Applications, Systems and Control: Foundations and Applications, pp.191-208, 1999. ,
A geometric characterization of viable sets for controlled degenerate diffusions. Set-Valued Analysis, vol.10, pp.129-141, 2002. ,
A representation formula for the mean curvature motion, SIAM Journal on Mathematical Analysis, vol.33, issue.4, pp.827-846, 2001. ,
Viability of open sets for stochastic optimal control, 2017. ,
Existence of stochastic control under state constraints, Comptes Rendus de l'Académie des Sciences -Series I -Mathematics, vol.327, issue.1, pp.17-22, 1998. ,
Invariant measures associated to degenerate elliptic operators, Indiana University Mathematics Journal, vol.59, issue.1, pp.53-78, 2010. ,
DOI : 10.1512/iumj.2010.59.3886
URL : http://www.mat.uniroma2.it/~cannarsa/cadpfr_indiana.pdf
Viability, invariance and applications, NorthHolland Mathematics Studies, vol.207, 2007. ,
Convergence of stochastic gene networks to hybrid piecewise deterministic processes, The Annals of Applied Probability, vol.22, issue.5, p.2012 ,
URL : https://hal.archives-ouvertes.fr/hal-00553482
Hybrid stochastic simplifications for multiscale gene networks, BMC Systems Biology, p.89, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00784449
Piecewise-deterministic Markov-processes -A general-class of non-diffusion stochastic-models, Journal of the Royal Statistical Society Series B-Methodological, vol.46, issue.3, pp.353-388, 1984. ,
Markov models and optimization, Monographs on Statistics and Applied Probability. Chapman & Hall, vol.49, 1993. ,
Shape analysis via oriented distance functions, Journal of Functional Analysis, vol.123, issue.1, pp.129-201, 1994. ,
DOI : 10.1006/jfan.1994.1086
URL : https://doi.org/10.1006/jfan.1994.1086
Optimal control of piecewise deterministic Markov processes, Applied stochastic analysis, vol.5, pp.303-325, 1989. ,
Compactification methods in the control of degenerate diffusions: existence of an optimal control, Stochastics, vol.20, issue.3, pp.169-219, 1987. ,
A class of stochastic differential equations with non-lipschitzian coefficients: pathwise uniqueness and no explosion, Comptes Rendus Mathematique, vol.337, issue.11, pp.737-740, 2003. ,
A study of a class of stochastic differential equations with non-lipschitzian coefficients. Probability Theory and Related Fields, vol.132, pp.356-390, 2005. ,
Viability for constrained stochastic differential equations, Differential Integral Equations, vol.6, issue.6, pp.1395-1414, 1993. ,
Invariance and Reachability for Controlled Piecewise Deterministic Markov Processes Associated to Gene Networks. ESAIM-Control Optimisation and Calculus of Variations, vol.18, pp.401-426, 2012. ,
DOI : 10.1051/cocv/2010103
URL : https://hal.archives-ouvertes.fr/hal-00727725
Asymptotic control for a class of piecewise deterministic markov processes associated to temperate viruses, SIAM Journal on Control and Optimization, vol.53, issue.4, pp.1860-1891, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01089528
Some applications of linear programming formulations in stochastic control, Journal of Optimization Theory and Applications, vol.155, issue.2, pp.572-593, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00759473
Noise-based switches and amplifiers for gene expression, vol.97, pp.2075-2080, 2000. ,
DOI : 10.1073/pnas.040411297
URL : http://www.pnas.org/content/97/5/2075.full.pdf
, Stochastic Differential Equations and Diffusion Processes, vol.24, 1981.
On the rate of convergence of finite-difference approximations for Bellman's equations with variable coefficients, Probab. Theory Related Fields, vol.117, issue.1, pp.1-16, 2000. ,
Uniqueness theorems and successive approximations, Annals of Mathematics, vol.50, issue.3, pp.722-730, 1949. ,
Two classes of quasi-steady-state model reductions for stochastic kinetics, The Journal of Chemical Physics, vol.127, issue.9, p.94106, 2007. ,
Uber die lage derintegralkurven gewhnlicher differentialgleichungen, Proc. Phys. Math. Soc. Japan, vol.24, pp.551-559, 1942. ,
Deterministic characterization of viability for stochastic differential equation driven by fractional brownian motion, ESAIM: COCV, vol.18, issue.4, pp.915-929, 2012. ,
The viability property of controlled jump diffusion processes, Acta Math. Sin. (Engl. Ser.), vol.24, issue.8, pp.1351-1368, 2008. ,
Optimal control with state-space constraint, II. SIAM J. Control Optim, vol.24, issue.6, pp.1110-1122, 1986. ,
DOI : 10.1137/0324032