Some Results on Backward Stochastic Differential Equations of Fractional Order

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Mahmudov N., Ahmadova A.

Qualitative Theory of Dynamical Systems, vol.21, no.4, 2022 (SCI-Expanded, Scopus)

• Nəşrin Növü: Article / Article
• Cild: 21 Say: 4
• Nəşr tarixi: 2022
• Doi nömrəsi: 10.1007/s12346-022-00657-z
• 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, Fractional backward stochastic differential equations, Weighted norm, Well-posedness
• Açıq Arxiv Kolleksiyası: Məqalə
• Adres: Yox

Qısa məlumat

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∈(12,1) 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.