The existence and uniqueness of the solution of an integral equation driven by a p-semimartingale of special type

By Kestutis Kubilius. 2002

62 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ed61c7c86a45498b06e79f24c4f71a7dff35957b

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In Applied Mathematics

In Finance

Citations in the corpus

Averaging principle for fast-slow system driven by mixed fractional Brownian rough path (2020, background): “Kubilius [18] studies SDEs driven by both fBm and Bm, in the one-dimensional case, with no drift term.”
Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion (2008, methodology): “Kubilius has studied stochastic differential equations driven by both fBm and standard Brownian motion (see [ 13 ]), in the one dimensional case, with �W, �H independent of the time and with no drift term (b ≡ 0). In this setting, the author proves an existence and uniqueness result provided that �W”
Existence and Uniqueness of the Solution of Stochastic Differential Equation Involving Wiener Process and Fractional Brownian Motion with Hurst Index H > 1/2 (2011, unknown): “Unique solvability or (1) was proved in [8] for time-independent coefficients and zero drift, [10] forH ∈ (3/4, 1) and bounded coefficients, and in [5] for anyH > 1/2, but under the assumption that W and B are independent.”
Controlled differential equations as Young integrals: A simple approach (2010, background): “The properties of such equations are studied for example in [1, 5, 6, 8, 14, 15, 25–30, 32, 35].”
Averaging dynamics driven by fractional Brownian motion (2019, methodology): “t witheachotherhowever, asolution theorywithmixedYoung andItôintegrals must be used. Such a theory is available in the literature, see for example the work by Guerra–Nualart [GN08] extending Kubilius [Kub02], as well as [dSEE18]. Our maintheoremisthefollowingresult,whichisaslightreformulation ofTheo”