Paracontrolled distribution approach to stochastic Volterra equations

[摘要] 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 Levy processes. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-25

[关键词] Fractional Brownian motion;Gaussian process;Ito-Lyons map;Paradifferential calculus;Rough differential equation;Stochastic Volterra equation