Picard Approximation of a Singular Backward Stochastic Nonlinear Volterra Integral Equation

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Ahmadova A., Mahmudov N.

Qualitative Theory of Dynamical Systems, vol.23, no.4, 2024 (SCI-Expanded) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 23 Say: 4
  • Nəşr tarixi: 2024
  • Doi nömrəsi: 10.1007/s12346-024-01043-7
  • jurnalın adı: Qualitative Theory of Dynamical Systems
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Açar sözlər: Adapted process, Backward stochastic nonlinear Volterra integral equation, Carathéodory conditions, Existence and uniqueness, Picard iteration, Singular backward stochastic equations
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

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∈(12,1) under a weaker condition than Lipschitz one in Hilbert space.