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Literature Cited
P. Billingsley, “Convergence of probability measures,” New York: Wiley (1968).
A. Bensoussan, “On the theory of option pricing” Acta Aplicandae Mathematicae,2, 139–158 (1984).
C. Dellacherie and P. A. Meyer, Probabilitiés et Potentiel, Herman Act. Sc. et. Ind. Paris, 1385 (1980).
M. Emery, “Stabilité des solutions des équations differentielles stochastiques: application aux integrales multiplicatives stochastiques,” Z. Wahrsch. Verw. Geb.,41, 241–262 (1978).
M. Emery, “Equations différentielles lipschitzinennes: étude de la stabilité,” Lecture Notes in Math., Springer-Verlag,714 (1979).
N. Ikeda and S. Watanabe, “Stochastic differential equations and diffusion processes,” Amsterdam: North-Holland (1981).
J. Jacod, “Calcul stochastique et problemes de martingales,” Lecture Notes in Math., Springer-Verlag,714 (1979).
J. Jacod, “Théorémes limite pour les processus,” Lecture Notes in Math., Springer-Verlag,1117, 299–409 (1983).
J. Jacod and J. Memin, “Weak and strong solutions of stochastic differential equations: existence and stability,” Lecture Notes in Maths. (Stochastic Integrals), Springer-Verlag,851, 169–212 (1981).
J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes. Berlin: Springer-Verlag (1987).
P. Kind, “Option valuation in a continuous-time conditional variance model of asset price returns,” Univ. of Chicago, Department of Economics, Preprint (1988).
G. Letta, “Martingales et integration stochastique,” Quaderni della Scuola Normale Superiore, Pisa (1984).
R. Sh. Liptser and A. N. Shiryaev, Theory of Martingales, North-Holland, Kluwer Acad. Publ. (1989).
D. L. McLeish, “An extended martingale principle,” Ann. Probab.,6, 144–150 (1978).
M. Métivier, “Sufficient conditions for tightness and weak convergence of a sequence of processes,” Univ. of Minnesota, Internal Report 55455 (1979).
M. Métivier, Semimartingales, a Course on Stochastic Processes, Berlin; New York: W. de Gruyter (1982).
M. Métivier, “Stability theorems for stochastic integral equations driven by random measures and semimartingales,” J. Integral Equations,3, 109–135 (1981).
M. Métivier and J. Pellaumail, Stochastic Integration, Academic Press (1980).
L. Pratelli, “Invariance des notions de semimartingale et d'integrale stochastique par un changement d'espace,” Pub. Dip. Mat. Univ. di Pisa, No. 262 (1988).
Ph. Protter, “HP stability of solutions of stochastdic differential equations,” Z. Wahrsch. Verw. Geb.,44, 337–352 (1978).
R. Rebolledo, “La méthode des martingales appliquée à l'etude de la convergence en loi des processus,” Mem. Soc. Math., France, No. 62 (1979).
R. Rebolledo, “Central limit theorems for local martingales,” Z. Wahrsch. Verw. Geb.,51, 269–286 (1980).
L. C. G. Rogers and D. Williams, Diffusions, Markov Processes and Martingales, J. Wiley and Sons (1987).
L. Slominski, “Stability of strong solution sof stochastic differential equations,” Stochastic Processes Appl.,31, 173–202 (1989).
F. Topsoe, “Topology and measure,” Lecture Notes in Math., Springer-Verlag,133 (1970).
K. Yamada, “A stability theorem for stochastic differential equations and application to stochastic control problems,” Stochastics,13, 257–279 (1984).
K. Yamada, “A stability theorem for stochastic differential equations with application to storage processes, random walks and optimal stochastic control problems,” Stochastic Processes Appl.,23, 199–220 (1986).
P. A. Zanzotto, “On the stability of stochastic differential equations ‘with memory’,” Rend. Acc. Naz. Sc. detta dei XL.,XIII (1989).
P. A. Zanzotto, “A stability theorem for a class of stochastic differential equations ‘with memory’,” Rend. Acc. Naz. Sc. detta dei XL,XIII (1989).
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Dipartimento di Matematica, Via Buonarroti, 2-56100 Pisa, Italy. Published in Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 31, No. 2, pp. 282–301, April–June, 1991.
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Zanzotto, P.A. An extension of a theorem of K. Yamada to equations “with memory”. Lith Math J 31, 188–204 (1991). https://doi.org/10.1007/BF00970816
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DOI: https://doi.org/10.1007/BF00970816