Abstract
We mainly study the existence and uniqueness of solutions to one-dimensional backward stochastic differential equations with terminal values satisfying a critical integrability and infinite time horizon. The main result is established under the assumption that the generator f exhibits a time-varying monotonicity in y and uniform continuity in z and the terminal value is required to satisfy the critical Lexp(μ02log(1+L))-integrability for a μ0>0, a condition stronger than LlogL-integrability but weaker than Lp(p>1)-integrability.
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