A multidimensional singular stochastic control problem on a finite time horizon
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Budhiraja, A., Ross, K., Existence of optimal controls for singular control problems with state constraints, Ann. Appl. Probab. 16, No. 4 (2006), 2235–2255.
Chow, P. L., Menaldi, J. L., Robin, M., Additive control of stochastic linear systems with finite horizon, SIAM J. Control Optim. 23, No.6 (1985), 858–899.
Dufour, F., Miller, B., Singular stichastic control problems, SIAM J. Control Optim. 43, No. 2 (2004), 708–730.
Evans, L. C., Partial Differential Equations, American Mathematical Society, Providence, RI, 1998.
Fleming, W. H., Soner, H. M., Controlled Markov Processes and Viscosity Solutions, Springer, New York, 2006.
Haussman, U. G., Suo, W., Singular optimal stochastic controls. I. Existence, SIAM J. Control Optim. 33, No. 3 (1995), 916–936.
Karatzas, I., Shreve, S. E., Brownian Motion and Stochastic Calculus, Springer-Verlag, New York, 1988.
Kruk, Ł., Optimal policies for n-dimensional singular stochastic control problems, Part I: The Skorokhod problem, SIAM J. Control Optim. 38, No. 5 (2000), 1603–1622.
Kruk, Ł., Optimal policies for n-dimensional singular stochastic control problems, Part II: The radially symmetric case. Ergodic control, SIAM J. Control Optim. 39, No. 2 (2000), 635–659.
Krylov, N. V., Controlled Diffusion Processes, Springer-Verlag, New York, 1980.
Menaldi, J. L., Taksar, M. I., Optimal correction problem of a multidimensional stochastic system, Automatica J. IFAC 25, No. 2 (1989), 223–232.
Rudin, W., Functional Analysis, McGraw-Hill Book Company, New York, 1991.
Rudin, W., Principles of Mathematical Analysis, McGraw-Hill Book Company, New York, 1976.
Soner, H. M., Shreve, S. E., Regularity of the value function for a two-dimensional singular stochastic control problem, SIAM J. Control Optim. 27 (1989), 876–907.
Soner, H. M., Shreve, S. E., A free boundary problem related to singular stochastic control, Applied stochastic analysis (London, 1989), Stochastics Monogr. 5, Gordon and Breach, New York, 1991, 265–301.
Soner, H. M., Shreve, S. E., A free boundary problem related to singular stochastic control: the parabolic case, Comm. Partial Differential Equations 16 (1991), 373–424.
S. A. Williams, P. L. Chow and J. L. Menaldi, Regularity of the free boundary in singular stochastic control, J. Differential Equations 111 (1994), 175–201.
http://en.wikipedia.org/wiki/Gronwall’s inequality, 24.09.2013.
DOI: http://dx.doi.org/10.17951/a.2015.69.1.23
Date of publication: 2015-11-30 09:21:11
Date of submission: 2015-09-03 12:17:00
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