Some Results on Backward Stochastic Differential Equations of Fractional Order

• Nazim I. Mahmudov ^[1] ; Arzu Ahmadova ^[2]
  1. [1] Eastern Mediterranean University

     Eastern Mediterranean University

     Chipre

     
  2. [2] Eastern Mediterranean University & University of Duisburg-Essen
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
• Idioma: inglés
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• Resumen

  • In this article, we deal with fractional stochastic differential equations, so-called Caputo type fractional backward stochastic differential equations (Caputo fBSDEs, for short), and study the well-posedness of an adapted solution to Caputo fBSDEs of order α ∈ ( 1 2 , 1) whose coefficients satisfy a Lipschitz condition. A novelty of the article is that we introduce a new weighted norm in the square integrable measurable function space that is useful for proving a fundamental lemma and its well-posedness. For this class of systems, we then show the coincidence between the notion of stochastic Volterra integral equation and the mild solution.