Picard Approximation of a Singular Backward Stochastic Nonlinear Volterra Integral Equation

• Autores: Arzu Ahmadova, Nazim I. Mahmudov
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 4, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-01043-7
• Enlaces
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• Resumen

  • 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.

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