Comparison theorem for solutions of backward stochastic differential equations with continuous coefficient
โ Scribed by Jicheng Liu; Jiagang Ren
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 106 KB
- Volume
- 56
- Category
- Article
- ISSN
- 0167-7152
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โฆ Synopsis
Comparison theorems for solutions of one-dimensional backward stochastic di erential equations were established by Peng and Cao-Yan, where the coe cients were, respectively, required to be Lipschitz and Dini continuous. In this work, we generalize the comparison theorem to the case where the coe cient is only continuous.
๐ SIMILAR VOLUMES
We prove the existence of a solution for "one dimensional" backward stochastic differential equations where the coefficient is continuous, it has a linear growth, and the terminal condition is squared integrable. We also obtain the existence of a minimal solution.
Existence and uniqueness is established for solutions to backward stochastic di erential equations with jumps and non-Lipschitzian coe cients in Hilbert space. The results are used to solve some special types of optimal stochastic control problems with respect to certain BSDEs with jumps in Hilbert