Preview
Unable to display preview. Download preview PDF.
References
Barlow, M.T. and Yor, M.: (Semi-) Martingale inequalities and local times, Z. Wahr. verw. Geb., 55 (1981), 237–254.
Situ Rong: On Strong solutions and stochastic (pathwise) Bang-Bang control for a non-linear system, 9th World Congrees of IFAC, Budapest, 2–6 July, 1984, Preprints, Vol. V, 24–29.
Situ Rong: On strong solutions, absolute continuity between solution measures and Bayes formula for stochastic differential equations with non-Lipschitz coefficients, Math. & Mech. Res. Report (Preprint) Zhongshan Univ. No. 1 (1981), Dec., 75–108.
Yamada, T. and Watanabe, S.: On the uniqueness of solutions of stochastic differential equations, I, II, J. Math. Kyoto Univ. Vol. 11, No. 1 (1971), 155–167; Vol. 11, No. 3 (1971), 553–563.
Ikeda, N. and Watanabe, S.: A comparison theorem for solutions of stochastic differential equations and its applications, J. Math. Kyoto Univ. 13–3 (1973), 497–512.
Ikeda, N. and Watanabe, S.: Stochastic Differential Equations and Diffusion processes, North-Holland/Kodansha, (1981).
Krylov, N. and Pragarauskas, H.: On the Bellman equation for uniformly non-degenerated general stochastic processes, Litovskii Matematicheskii Sbornik Vol. 20, No. 1, pp. 85–98, January–March, 1980 (in Russian).
Mel'nikov, A.V.: Stochastic equations and Krylov's estimates for Semi-martingales, Stochastic, Vol. 10 (1983), pp. 81–102.
Chitashvili, R.J. and Toronjadze, T.A.: On one-dimensional stochastic differential equations with unit diffusion coefficient, structure of solutions, Stochastic, Vol. 4, No. 4 (1981), 281–315.
Jacod, J.: Calcul Stochastique et Problemes de Martingales, Lecture Notes in Mathematics 714 (1979), Springer-Verlag, New York.
Marhno, S.: On the existence and uniqueness of weak solutions for stochastic equations, Theory of Stochastic Processes 5 (1977), Naoka Domka Kiev, 68–76 (in Russian).
Marhno, S.: On weak solutions of stochastic differential equations, Probability Theory and Mathematical Statistics — Contiguous Natural Sciences Collection, Vol. 13, Published by Kiev National University, Kiev (1975), 106–115, (in Russian).
Zvonkin, A.V.: A transformation of the phase space of a diffusion process that remove the drift, Math. USSR Sbornik Vol. 22 (1974), No. 1, 129–149.
Gal'cuk, L.I.: A comparison theorem for stochastic equations with integrals on martingales and random measures, Prob. Th. Appl. 27 (1982), No. 3, 425–433.
Gihman, I.I. and Skorohod, A.V.: Stochastic Differential Equations and its Applications, Naokoba Domka, Kiev, (1982), (in Russian).
Barlow, M. and Perkins, E.: One dimensional stochastic differential equations involving a singular increasing process (1983), to appear.
Meyer, P.A.: Un cours sur les integrales stochastiques, Sem. Prob. Strasbourg X, Lect. Notes in Math. 511, Springer-Verlag, Berlin-Heidelberg-New-York, 1976.
Barlow, M.: One dimensional stochastic differential equations with no strong solutions, J. London Math. Soc. (2), 26 (1982), 335–347.
Mckean, H.P.: Stochastic Integrals, Academic Press, New York, 1969.
Anulova, S.V. and Pragarauskas, H.: On weak Markovian solutions of stochastic equations, Liet. Mat. Rink., 17, No. 2 (1977), 5–26.
Benes, V.E. and Karatzas, I.: Examples of optimal control for partially observable systems: comparison, classical, and martingale methods, Stochastic 5 (1981), 43–64.
Balakrishnan, A.V.: On stochastic Bang Bang control. Appl. Math. Optim. 6 (1980), 91–96.
Ruzicka, J.: On the separation principle with bounded controls, Appl. Math. Optim. 3 (1977), 243–261.
Situ Rong: Non-convex stochastic optimal control and maximum principle, Control of Distributed Parameter Systems (1982) — Proceedings of the Third IFAC Symposium, Toulouse, France, 29 June — 2 July 1982, ed. J.-P. Babary and L.L. Letty, Pergamon Press, 401–407.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verlag
About this paper
Cite this paper
Rong, S. (1985). On strong solution, uniqueness, stability and comparison theorems for a stochastic system with poisson jumps. In: Kappel, F., Kunisch, K., Schappacher, W. (eds) Distributed Parameter Systems. Lecture Notes in Control and Information Sciences, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0005662
Download citation
DOI: https://doi.org/10.1007/BFb0005662
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15872-1
Online ISBN: 978-3-540-39661-1
eBook Packages: Springer Book Archive