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Mathematics > Probability

arXiv:1812.05456 (math)
[Submitted on 13 Dec 2018 (v1), last revised 30 Sep 2019 (this version, v2)]

Title:Paracontrolled distribution approach to stochastic Volterra equations

Authors:David J. Prömel, Mathias Trabs
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Abstract:Based on the notion of paracontrolled distributions, we provide existence and uniqueness results for rough Volterra equations of convolution type with potentially singular kernels and driven by the newly introduced class of convolutional rough paths. The existence of such rough paths above a wide class of stochastic processes including the fractional Brownian motion is shown. As applications we consider various types of rough and stochastic (partial) differential equations such as rough differential equations with delay, stochastic Volterra equations driven by Gaussian processes and moving average equations driven by Lévy processes.
Comments: 39 pages
Subjects: Probability (math.PR); Classical Analysis and ODEs (math.CA); Functional Analysis (math.FA)
Cite as: arXiv:1812.05456 [math.PR]
  (or arXiv:1812.05456v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1812.05456
Journal reference: J. Differential Equations, vol. 302, p. 222--272, 2021

Submission history

From: David J. Prömel [view email]
[v1] Thu, 13 Dec 2018 14:34:13 UTC (41 KB)
[v2] Mon, 30 Sep 2019 11:54:45 UTC (41 KB)
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