Weak solution for stochastic differential equations with terminal conditions
- 128 Downloads
The notion of weak solution for stochastic differential equation with terminal conditions is introduced. By Girsanov transformation, the equivalence of existence of weak solutions for two-type equations is established. Several sufficient conditions for the existence of the weak solutions for stochastic differential equation with terminal conditions are obtained, and the solution existence condition for this type of equations is relaxed. Finally, an example is given to show that the result is an essential extension of the one under Lipschitz condition ong with respect to (Y,Z).
Keywordsstochastic differential equation with terminal condition weak solution strong solution Novikov condition
Unable to display preview. Download preview PDF.
- 2.Huang, Z. Y., Foundations of Stochastic Analysis, Wuhan: Wuhan University Press, 1988.Google Scholar
- 3.Skorohod, A. V., Studies in the Theory of Random Procosses, Reading, Mass: Addison Wesley, 1965.Google Scholar
- 4.Stroock, D. W., Varadhan, S. R. S., Multidimensional Duffusion Processes, Berlin: Springer, 1979.Google Scholar
- 7.Kunita, H., Stochastic Flows and Stochastic Differential Equation, Cambridge: Cambridge Univ. Press, 1990.Google Scholar
- 12.Huang, Z. Y., Lin, Q Q., The weak solution for stochastic differential equations with terminal conditions, Applied Math., 1997, 10(3): 56–59.Google Scholar
- 13.Peng, S. G., Backward SDE and related g-expectation, in Backward Stochastic Differential Equations (eds. Karoui, E. L., Mazliak, L.), London: Addison-Wesley-Longman, 1997, 141–159.Google Scholar
- 14.Karoui, N. E. L., Mazliak, L, Backward Stochastics Differential Equations, Pitman Research Notes in Mathematics, Series 364, London: Addison-Wesley-Longman, 1997.Google Scholar
- 15.Ma, J., Yong, J., Forward-Backward Stochastics Differential Equations and Their Applications, LNM, Vol. 1702, New York: Springer, 1999.Google Scholar