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Abstrakty
The properties of value functions of time inhomogeneous optimal stopping problem and zero-sum game (Dynkin game) are studied through time dependent Dirichlet form. Under the absolute continuity conditio on the transition function of the underlying process and some other assumptions, the refined solutions without exceptional starting points are proved to exist, and the value functions of the optimal stopping problem and zero-sum game, which belong to certain functional spaces, are characterized as the solutions of some variational inequalities, respectively.
Czasopismo
Rocznik
Tom
Strony
253--271
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
- Department of Mathematics, University of Houston-Clear Lake, Houston, Texas, 77058
Bibliografia
- [1] M. Fukushima, On two classes of smooth measures for symmetric Markov processes, in: Stochastic Analysis, M. Métivier and S. Watanabe (Eds.), Lecture Notes in Math., Vol. 1322, Springer, 1988, pp. 17-27.
- [2] M. Fukushima and K. Menda, Refined solutions of optimal stopping games for symmetric Markov processes, Technology Reports of Kansai University, 48 (2006), pp. 101-110.
- [3] M. Fukushima, Y. Ōshima, and M. Takeda, Dirichlet Forms and Symmetric Markov Processes, second edition, de Gruyter, Berlin-New York 2011.
- [4] M. Fukushima and M. Taksar, Dynkin games via Dirichlet froms and singular control of one-dimensional diffusions, SIAM J. Control Optim. 41 (3) (2002), pp. 682-699.
- [5] D. Lamberton, Optimal stopping with irregular reward functions, Stochastic Process. Appl. 119 (2009) pp. 3253-3284.
- [6] Z.-M. Ma and M. Röckner, An Introduction to the Theory of (Non-symmetric) Dirichlet Forms, Springer, Berlin 1992.
- [7] H. Nagai, On an optimal stopping problem and a variational inequality, J. Math. Soc. Japan 30 (1978), pp. 303-312.
- [8] Y. Oshima, Time dependent Dirichlet forms and related stochastic calculus, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 7 (2004), pp. 281-316.
- [9] Y. Oshima, On an optimal stopping problem of time inhomogeneous diffusion processes, SIAM J. Control Optim. 45 (2) (2006), pp. 565-579.
- [10] J. Palczewski and L. Stettner, Finite horizon optimal stopping of time-discontinuous functionals with applications to impulse control with delay, SIAM J. Control Optim. 48 (8) (2010), pp. 4874-4909.
- [11] J. Palczewski and L. Stettner, Stopping of functionals with discontinuity at the boundary of an open set, Stochastic Process. Appl. 121 (2011), pp. 2361-2392.
- [12] W. Stannat, The Theory of Generalized Dirichlet Forms and Its Applications in Analysis and Stochastics, Mem. Amer. Math. Soc., Vol. 142 (678), American Mathematical Stociety, 1999.
- [13] L. Stettner, Zero-sum Markov games with stopping and impulsive strategies, Appl. Math. Optim. 9 (1982), pp. 1-24.
- [14] L. Stettner, Penalty method for finite horizon stopping problems, SIAM J. Control Optim. 49 (3) (2011), pp. 1078-1099.
- [15] J. Zabczyk, Stopping games for symmetric Markov processes, Probab. Math. Statist. 4 (2) (1984), pp. 185-196.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
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Bibliografia
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bwmeta1.element.baztech-d3e0acc0-66e6-4624-846d-6f848f5f7191