| Abstract: |
| In the theory of BSDEs, in order to guarantee the existence and uniqueness of adapted solutions to BSDEs, one usually supposes that the generator g is Lipschitz with respect to y and z or other similar hypothetical conditions in which the variable z satisfies the similar assumptions as the variable y. In this talk, we show that BSDEs also has a unique adapted solution if the generator g is Lipchitz with respect to y and is linear growth and continuous with respect to z. This implies that the variable z is determined by y. And as an application, we obtain that the corresponding partial differential equations have a unique viscosity solution. |
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