Resumen de Picard Approximation of a Singular Backward Stochastic Nonlinear Volterra Integral Equation

Arzu Ahmadova, Nazim I. Mahmudov

• In this paper we prove that Picard iterations of BSDEs with globally Lipschitz continuous nonlinearities converge exponentially fast to the solution. Our main result in this paper is to establish a fundamental lemma to prove the global existence and uniqueness of an adapted solution to a singular backward stochastic nonlinear Volterra integral equation (for short, singular BSVIE) of order α ∈ ( 1 2 , 1) under a weaker condition than Lipschitz one in Hilbert space.