A New Approach to BSDE (Backward Stochastic Differential by Lixing, Jin
By Lixing, Jin
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Extra info for A New Approach to BSDE (Backward Stochastic Differential Equation)
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M . Our contribution in this aspect is the the following lemma which ﬁlls in the gap in their proof. If L satisﬁes local, homogeneous and K − Lipschitz conditions, then for any 34 nonnegative predictable process Y ˆ t1 KE[ ⟨ Ys d M − M 1 t2 2 ˆ ⟩ s ]≥E t1 Ys2 | L[t2 ,t1 ] (M 1 )s − L[t2 ,t1 ] (M 2 )s |2 ds, t2 where K − Lipschitz condition property means there is a positive constant K such that for any 0 ≤ t2 ≤ t1 ≤ T and any M1 , M2 ∈ M2 ([t2 , t1 ], Rn ), ⟨ ⟩ ⟨ ⟩ KE[ M 1 − M 2 t1 − M 1 − M 2 t2 ] ≥ ˆ t1 | L(M 1 )s − L(M 2 )s |2 ds.