Optimal evasion of a diffusion process from stable deterministic pursuit. (English) Zbl 0587.60075
Translation from Probl. Ustojch. Stokhasticheskikh Modelej 1983, 108-116 (Russian) (1983; Zbl 0567.60078).
MSC:
| 60J60 | Diffusion processes |
| 60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |
Keywords:
parabolic Kolmogorov equationReferences:
| [1] | H. J. Kushner, Stochastic Stability and Control [Russian translation], Mir, Moscow (1969). |
| [2] | Pan-Tai-Liu, ?Stochastic pursuit-evasion games,? J. Math. Anal. Appl.,59, 301?309 (1977). · Zbl 0392.93028 · doi:10.1016/0022-247X(77)90110-X |
| [3] | N. N. Krasovskii, ?On a pursuit problem,? Prikl. Mat. Mekh.,26, No. 2, 218?232 (1962). |
| [4] | I. D. Cherkasov, ?Prolongation of lifetime of diffusion processes,? in: Stochastic Processes and Control (1977), pp. 65?94. |
| [5] | I. D. Cherkasov, ?The separation method in the theory of multidimensional Markov processes,? Izv. Yassy (Iasi) Polytechnical Institute,4, No. 2, 23?32 (1958). |
| [6] | W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer-Verlag, New York-Berlin (1975). · Zbl 0323.49001 |
| [7] | R. Z. Khas’minskii, ?Stability of the paths of Markov processes,? Prikl. Mat. Mekh.,26, No. 6, 1025?1032 (1962). |
| [8] | G. Tintner and R. C. Patel, ?Multivariate lognormal diffusion process of economic development,? Oper. Res., Verfahren,14, 232?246, Meisenheim (1972). · Zbl 0255.90006 |
| [9] | A. M. Lyapunov, Collected Works [in Russian], Vol. 2, Moscow (1956). · Zbl 0192.31202 |
| [10] | R. Z. Khas’minskii, Stability of Systems of Differential Equations under Random Disturbances of Their Parameters [in Russian], Nauka, Moscow (1969). |
| [11] | I. D. Cherkasov, ?On Bachelier-type stochastic processes,? Revue Roumaine de Mathematiques Pures et Appliquees,9, No. 9, 849?857 (1964). |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
