Efficient simulation of a new class of Volterra-type SDEs

Ofelia Bonesini; Giorgia Callegaro; Martino Grasselli; Gilles Pagès

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arXiv · 2306.02708

Efficient simulation of a new class of Volterra-type SDEs

Ofelia Bonesini·Giorgia Callegaro·Martino Grasselli·Gilles Pagès

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Abstract

We propose a new theoretical framework that exploits convolution kernels to transform a Volterra-type path-dependent (non-Markovian) stochastic process into a standard (Markovian) diffusion process. Remarkably, it is also possible to go back, i.e., the transformation is reversible. We discuss existence and path-wise regularity of solutions for our class of stochastic differential equations. In the fractional kernel case, when $H \in (0,\frac12)$, where $H$ is the Hurst coefficient, we propose a numerical simulation scheme which exhibits a remarkable strong convergence rate of order $1/2$, which constitutes a bold improvement when compared with the performance of available Euler schemes, whose strong rate of convergence is $H$.

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Ofelia Bonesini, Giorgia Callegaro, Martino Grasselli, Gilles Pagès. 2023-06-05. Efficient simulation of a new class of Volterra-type SDEs. https://arxiv.org/abs/2306.02708

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