Abstract
In this work we construct a branching diffusion process whose “individuals” are interdependent, as the unique solution of a martingale problem. As an application we propose and solve a closed loop, finite horizon optimal control problem.
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References
J. M. Bismut, “Théorie Probabiliste de Contrôle des Diffusions,” Memoirs of the American Mathematical Society,4, 167 (1976).
J. M. Bismut, Control of Jump Processes, à paraître.
R. M. Blumenthal, and R. K. Getoor,Markov Processes and Potential Theory, Academic Press (1968).
E. B. Dynkin,Markov Processes, Vol. I & II, Springer-Verlag (1965).
N. Ikeda, M. Nagasawa, S. Watanabe, “Branching Markov Processes I, II, III,” J. Math. Kyoto Univ.8, 233–278 (1968);8, 365–410 (1968);9, 95–160 (1969).
N. Ikeda, M. Nagsawa, S. Watanabe, Correction to “Branching Markov Processes II,” J. Math. Kyoto Univ.11, 195–196 (1971).
P. A. Meyer, “Intégrales stochastiques I, II, III,” Séminaire de Probabilitiés, no. 1, 72–111. Springer-Verlag, Lecture Notes in Mathematics No. 39.
P. A. Meyer, “Un cours sur les Intégrales Stochastiques,” Séminaire de Probabilitiés, No. 10, 245–400. Springer-Verlag. Lecture Notes in Mathematics, No. 511.
P. A. Meyer, “La Théorie de la Prédiction de F. Knight,” Séminaire de Probabilitiés, No. 10, 86–103. Springer-Verlag, Lecture Notes in Mathematics, No. 511.
P. A. Meyer, “Renaissance, Recollements, Mélanges, Ralentissement de Processus de Markov,” Ann. Inst. Fourier, Grenoble,25, 465–497 (1975).
P. Priouret, and P. Courrege, “Recollement de processus de Markov,” Publications de l'Institut de Statistique de l'Universite de Paris, XIV, 275–377 (1965).
T. Rolski, and R. Jankiewicz. “Piecewise Markov Processes on a General State Space” Zastosowania Matematyki-Applicationes Mathematicae XV,4, 421–436, (1977).
D. Stroock, and S. R. S. Varadhan, “Diffusion Processes with Continuous Coefficients,” Comm. Pure and Appl. Math.,22, 345–400, 479–530, (1969).
D. Stroock, and S. R. S. Varadhan, “Diffusion Processes with Boundary Conditions,” Comm. Pure and Appl. Math.,24, 147–225 (1971).
D. Stroock, and S. R. S. Varadhan, “On Degenerate Elliptic-Parabolic Operators of Second Order and Their Associated Diffusions,” Comm. Pure and Appl. Math.,25, 651–713 (1972).
D. Stroock, “Diffusion Processes Associated with Lévy Generators,” Zeitschrift für Wahrschein.verw.Gebiete32, 209–244 (1977).
D. H. Wagner, “Survey of Measurable Selection Theorems,” SIAM, J. Control & Optimization,15, 859–903 (1977).
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Communicated by W. Fleming
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Ustunel, S. Construction of branching diffusion processes and their optimal stochastic control. Appl Math Optim 7, 11–33 (1981). https://doi.org/10.1007/BF01442107
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DOI: https://doi.org/10.1007/BF01442107