Keywords
- Stochastic Differential Equation
- Strong Solution
- Finite Variation
- Predictable Process
- Canonical Decomposition
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A. BENSOUSSAN, R. TEMAM: Equations aux dérivées partielles stochastiques non linéaires. Israël J. Math. 11, 1972, 95–129.
P. BILLINGSLEY: Convergence of probability measures. Wiley and Sons: New-York, 1968.
C. DOLEANS-DADE: On the existence and unicity of solution of stochastic integral equations. Z. für Wahr. 34, 93–101, 1976.
C. DOLEANS-DADE, P.A. MEYER: Equations différentielles stochastiques. Sém. Probab. XI, Lect. Notes in Math. 581, 376–382, 1977.
M. EMERY: Une topologie sur l'espace des seminartingales. Sém. Probab. XIII, Lect. Notes in Math. 721, 260–281, 1979.
M. EMERY: Equations différentielles stochastiques lipschitziennes: étude de la stabilité. Sém. Probab. XIII, Lect. Notes in Math. 721 281–293, 1979.
B. GRIGELIONIS, R. MIKULEVICIUS: On weak convergence of semimartingales. Lit. Math. J. XXI, 1981.
I. GYONGY, N.V. KRYLOV: On stochastic equations with respect to semimartingales I, to appear, 1980.
J. JACOD: Calcul stochastique et problèmes de martingales. Lect. Notes in Math. 714, Springer Verlag: Berlin, 1979.
J. JACOD: Intégrales stochastiques par rapport à une semimartingale vectorielle et changements de filtration. Sém. Probab. XIV, Lect. Notes in Math. 784, 161–172, 1980.
J. JACOD: Weak and strong solutions of stochastic differential equations. Stochastics, 3, 171–191, 1980.
J. JACOD: Une condition d'existence et d'unicité pour les solutions fortes d'équations différentielles stochastiques. To appear in Stochastics, 1980.
J. JACOD, J. MEMIN: Existence of weak solutions for stochastic differential equations driven by semimartingales. To appear in Stochastics, 1980.
J. JACOD, J. MEMIN, M. METIVIER: Tightness and stopping times: some new conditions. To appear, 1980.
J. JACOD, J. MEMIN: Sur un type de convergence intermédiaire entre la convergence en probabilité et la convergence en loi. To appear in: Sém. de Probab. XV, 1980.
V.A. LEBEDEV: On the existence of a solution of the stochastic equation with respect to a martingale and a stochastic measure. Int. Symp. on Stoch. Diff. Equa., Vilnius, 65–69, 1978.
J. MEMIN: Espaces de semimartingales et changements de probabilité. Z. für Wahr. 52, 9–40, 1980.
M. METIVIER, J. PELLAUMAIL: Stochastic integration. To appear, 1980.
M. METIVIER, G. PISTONE: Sur une équation d'évolution stochastique. Bull. Soc. Math. France, 104, 65–85, 1976.
P.A. MEYER: Un cours sur les intégrales stochastiques. Sém. Probab. X, Lect. Notes in Math. 511, 245–400, 1976.
P.A. MEYER: Conergence faible et compacité des temps d'arrêt d'après Baxter et Chacon. Sém. Probab. XII, Lect. Notes in Math. 649, 411–423, 1978.
E. PARDOUX: Thèse, Univ. Paris-Sud, 1975.
J. PELLAUMAIL: Solutions faibles pour des processus discontinus. Comptes Rendus Acad. Sci. Paris (A) 290, 431–433, 1980.
P. PROTTER: On the existence, uniqueness, convergence and explosions of solutions of systems of stochastic differential equations. Ann. Probab. 5, 243–261, 1977.
B.L. ROZOVSKII: A note on strong solutions of stochastic differential equations with random coefficients. To appear: 1980.
A.V. SKOROKHOD: Limit theorems for stochastic processes. Theor. Probab. and Appl. 1, 261–290 (AMS Transl.) 1956.
C. STRICKER: Quasimartingales, martingales locales, semimartingales et filtrations. Z. für Wahr. 39, 55–63, 1977.
D.W. STROOCK, S.R.S. VARADHAN: Multidimensional diffusion processes. Springer Verlag: Berlin, 1979.
T. YAMADA, S. WATANABE: On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto Univ. 11, 156–167, 1971.
A. V. ZVONKIN, N.V. KRYLOV: On strong solutions of stochastic differential equations. School-Seminar (Druskininkai), Vilnius, Ac. Sci. Lit. SSR, II, 9–88, 1975.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer-Verlag
About this paper
Cite this paper
Jacod, J., Memin, J. (1981). Weak and strong solutions of stochastic differential equations: Existence and stability. In: Williams, D. (eds) Stochastic Integrals. Lecture Notes in Mathematics, vol 851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088728
Download citation
DOI: https://doi.org/10.1007/BFb0088728
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10690-6
Online ISBN: 978-3-540-38613-1
eBook Packages: Springer Book Archive
