Existence and smoothness of the density of the solution to fractional stochastic integral Volterra equations

Mireia Besalú; David Márquez-Carreras; Eulàlia Nualart

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arXiv · 1910.07288

Existence and smoothness of the density of the solution to fractional stochastic integral Volterra equations

Mireia Besalú·David Márquez-Carreras·Eulàlia Nualart

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Abstract

We consider stochastic Volterra integral equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 . We first derive supremum norm estimates for the solution and its Malliavin derivative. We then show existence and smoothness of the density under suitable nondegeneracy conditions. This extends the results in Hu-Nualart and Nualart-Saussereau where stochastic differential equations driven by fractional Brownian motion are considered. The proof uses a priori estimates for deterministic differential equations driven by a function in a suitable Sobolev space.

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Mireia Besalú, David Márquez-Carreras, Eulàlia Nualart. 2019-10-16. Existence and smoothness of the density of the solution to fractional stochastic integral Volterra equations. https://arxiv.org/abs/1910.07288

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