Free Access
Volume 26, 2020
Article Number 25
Number of page(s) 47
Published online 03 March 2020
  1. A. Almudevar, A dynamic programming algorithm for the optimal control of piecewise deterministic Markov processes. SIAM J. Control Opti. 40 (2001) 525–539. [CrossRef] [Google Scholar]
  2. S. Altay, K. Colaneri and Z. Eksi, Portfolio optimization for a large investor controlling market sentiment under partial information. SIAM J. Financ. Mat. 10 (2019) 512–546. [CrossRef] [Google Scholar]
  3. S. Asmussen, Applied Probability and Queues (Stochastic Modelling and Applied Probability). Vol. 51 of Applications of Mathematics, 2nd edn. Springer-Verlag, New York (2003). [Google Scholar]
  4. A. Bain and D. Crisan, Fundamentals of Stochastic Filtering. Springer, New York (2009). [CrossRef] [Google Scholar]
  5. E. Bandini, Constrained BSDEs driven by a non quasi-left-continuous random measure and optimal control of PDMPs on bounded domains. Preprint arXiv:1712.05205 (2017). [Google Scholar]
  6. E. Bandini, Optimal control of piecewise deterministic Markov processes: a BSDE representation of the value function. ESAIM: COCV 24 (2018) 311–354. [CrossRef] [EDP Sciences] [Google Scholar]
  7. E. Bandini and M. Fuhrman, Constrained BSDEs representation of the value function in optimal control of pure jump Markov processes. Stoch. Process. Appl. 127 (2017) 1441–1474. [CrossRef] [Google Scholar]
  8. E. Bandini, A. Cosso, M. Fuhrman and H. Pham, Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem. Stoch. Process. Appl. 129 (2019) 674–711. [CrossRef] [Google Scholar]
  9. E. Bandini, F. Confortola and A. Cosso, BSDE representation and randomized dynamic programming principle for stochastic control problems of infinite-dimensional jump-diffusions. Preprint arXiv:1810.01728 (2018). [Google Scholar]
  10. E. Bandini, A. Cosso, M. Fuhrman and H. Pham, Backward SDEs for optimal control of partially observed path-dependent stochastic systems: a control randomization approach. Ann. Appl. Probab. 28 (2018) 1634–1678. [Google Scholar]
  11. G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi. Vol. 17 of Mathematiques & Applications. Springer-Verlag, Paris (1994). [Google Scholar]
  12. A. Bensoussan, M. Çakanyıldırım and S.P. Sethi, On the optimal control of partially observed inventory systems. C. R. Math. Acad. Sci. Paris 341 (2005) 419–426. [CrossRef] [Google Scholar]
  13. A. Bensoussan, J. Frehse and P. Yam, Mean Field Games and Mean Field Type Control Theory. Springer Briefs in Mathematics. Springer, New York (2013). [CrossRef] [Google Scholar]
  14. D.P. Bertsekas and S.E. Shreve, Stochastic Optimal Control: The Discrete Time Case. Vol. 139 of Mathematics in Science and Engineering. Academic Press, Inc., New York, London (1978). [Google Scholar]
  15. V.I. Bogachev, Measure Theory, Vol. I, II. Springer-Verlag, Berlin (2007). [CrossRef] [Google Scholar]
  16. P. Brémaud, Point Processes and Queues. Springer Series in Statistics. Springer-Verlag, New York (1981). [CrossRef] [Google Scholar]
  17. A.E. Bryson, Jr. and D.E. Johansen, Linear filtering for time-varying systems using measurements containing colored noise. IEEE Trans. Automat. Contr. AC-10 (1965) 4–10. [Google Scholar]
  18. E. Buckwar and M.G. Riedler, An exact stochastic hybrid model of excitable membranes including spatio-temporal evolution. J. Math. Biol. 63 (2011) 1051–1093. [CrossRef] [PubMed] [Google Scholar]
  19. A. Calvia, Optimal control of continuous-time Markov chains with noise-free observation. SIAM J. Control Optim. 56 (2018) 2000–2035. [Google Scholar]
  20. C. Ceci and A. Gerardi, Filtering of a Markov jump process with counting observations. Appl. Math. Optim. 42 (2000) 1–18. [Google Scholar]
  21. C. Ceci and A. Gerardi, Nonlinear filtering equation of a jump process with counting observations. Acta Appl. Math. 66 (2001) 139–154. [Google Scholar]
  22. C. Ceci and A. Gerardi, Controlled partially observed jump processes: dynamics dependent on the observed history. In Vol 47 of Proceedings of the Third World Congress of Nonlinear Analysts, Part 4 Catania, 2000 (2001) 2449–2460. [Google Scholar]
  23. C. Ceci, A. Gerardi and P. Tardelli, Existence of optimal controls for partially observed jump processes. Acta Appl. Math. 74 (2002) 155–175. [Google Scholar]
  24. K. Colaneri, Z. Eksi, F. Rüdiger and M. Szölgyenyi, Optimal liquidation under partial information with price impact. Preprint arXiv:1606.05079v4 (2019). [Google Scholar]
  25. F. Confortola and M. Fuhrman, Filtering of continuous-time Markov chains with noise-free observation and applications. Stochastics 85 (2013) 216–251. [CrossRef] [Google Scholar]
  26. O.L.V. Costa and F. Dufour, Continuous Average Control of Piecewise Deterministic Markov Processes. Springer Briefs in Mathematics. Springer, New York (2013). [CrossRef] [Google Scholar]
  27. O.L.V. Costa, F. Dufour and A.B. Piunovskiy, Constrained and unconstrained optimal discounted control of piecewise deterministic Markov processes. SIAM J. Control Optim. 54 (2016) 1444–1474. [Google Scholar]
  28. M.G. Crandall, H. Ishii and P.-L. Lions, User’s guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. (N.S.) 27 (1992) 1–67. [CrossRef] [MathSciNet] [Google Scholar]
  29. D. Crisan, M. Kouritzin and J. Xiong, Nonlinear filtering with signal dependent observation noise. Electron. J. Probab. 14 (2009) 1863–1883. [Google Scholar]
  30. M.H.A. Davis, Control of piecewise-deterministic processes via discrete-time dynamic programming, in Stochastic Differential Systems (Bad Honnef, 1985). Vol. 78 of Lecture Notes in Control and Information Sciences. Springer, Berlin (1986) 140–150. [CrossRef] [Google Scholar]
  31. M.H.A. Davis and M. Farid, Piecewise-deterministic processes and viscosity solutions, in Stochastic Analysis, Control, Optimization and Applications. Systems Control Foundations and Applications. Birkhäuser Boston, Boston, MA (1999) 249–268. [Google Scholar]
  32. M.H.A. Davis, Markov Models and Optimization. Vol. 49 of Monographs on Statistics and Applied Probability. Chapman and Hall, London (1993). [Google Scholar]
  33. M.A.H. Dempster, Optimal control of piecewise deterministic Markov processes, in Applied Stochastic Analysis (London, 1989). Vol. 5 of Stochastics Monographs, Gordon and Breach, New York (1991) 303–325. [Google Scholar]
  34. R.J. Elliott, L. Aggoun and J.B. Moore, Hidden Markov Models: Estimation and Control. Vol. 29 of Applications of Mathematics (New York). Springer-Verlag, New York (1995). [Google Scholar]
  35. G. Fabbri, F. Gozzi and A. Swiech, Stochastic Optimal Control in Infinite Dimension: Dynamic Programming and HJB Equations, With a Contribution by Marco Fuhrman and Gianmario Tessitore. Vol. 82 of Probability Theory and Stochastic Modelling. Springer, Cham (2017). [CrossRef] [Google Scholar]
  36. W.H. Fleming and H.M. Soner, Controlled Markov Processes and Viscosity Solutions. Vol. 25 of Stochastic Modelling and Applied Probability, 2nd edn. Springer, New York (2006). [Google Scholar]
  37. L. Forwick, M. Schäl and M. Schmitz, Piecewise deterministic Markov control processes with feedback controls and unbounded costs. Acta Appl. Math. 82 (2004) 239–267. [Google Scholar]
  38. M. Jacobsen, Point Process Theory and Applications: Marked Point and Piecewise Deterministic Processes. Probability and Its Applications. Birkhäuser Boston, Inc., Boston, MA (2006). [Google Scholar]
  39. J. Jacod, Multivariate point processes: predictable projection, Radon-Nikodým derivatives, representation of martingales. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 31 (1974) 235–253. [CrossRef] [Google Scholar]
  40. M. Joannides and F. LeGland, Nonlinear filtering with continuous time perfect observations and noninformative quadratic variation, in Proceeding of the 36th IEEE Conference on Decision and Control (1997) 1645–1650. [CrossRef] [Google Scholar]
  41. I. Kharroubi and H. Pham, Feynman-Kac representation for Hamilton-Jacobi-Bellman IPDE. Ann. Probab. 43 (2015) 1823–1865. [Google Scholar]
  42. H. Körezlioğlu and W.J. Runggaldier, Filtering for nonlinear systems driven by nonwhite noises: an approximation scheme. Stoch. Stoch. Rep. 44 (1993) 65–102. [CrossRef] [Google Scholar]
  43. G. Last and A. Brandt, Marked Point Processes on the Real Line: The Dynamic Approach. Probability and Its Applications (New York). Springer-Verlag, New York (1995). [Google Scholar]
  44. R.H. Martin, Jr. Differential equations on closed subsets of a Banach space. Trans. Am. Math. Soc. 179 (1973) 399–414. [Google Scholar]
  45. J.R. Norris, Markov Chains. Vol. 2 of Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge (1998). [Google Scholar]
  46. V. Renault, M. Thieullen and E. Trélat, Optimal control of infinite-dimensional piecewise deterministic Markov processes and application to the control of neuronal dynamics via Optogenetics. Netw. Heterog. Media 12 (2017) 417–459. [CrossRef] [Google Scholar]
  47. L.C.G. Rogers and D. Williams, Diffusions, Markov processes, and Martingales (Foundations). Vol. 1 of Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, 2nd edn. John Wiley & Sons, Ltd., Chichester (1994). [Google Scholar]
  48. Y. Takeuchi and H. Akashi, Least-squares state estimation of systems with state-dependent observation noise. Automatica J. IFAC 21 (1985) 303–313. [CrossRef] [Google Scholar]
  49. D. Vermes, Optimal control of piecewise deterministic Markov process. Stochastics 14 (1985) 165–207. [CrossRef] [MathSciNet] [Google Scholar]
  50. J.T. Winter, Optimal Control of Markovian Jump Processes with Different Information Structures. Ph.D. thesis, Universität Ulm (2008). [Google Scholar]
  51. J. Xiong, An Introduction to Stochastic Filtering Theory. Oxford University Press, New York (2008). [Google Scholar]
  52. A.A. Yushkevich, On reducing a jump controllable Markov model to a model with discrete time. Theory Probab. Appl. 25 (1980) 58–69. [CrossRef] [Google Scholar]

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