6 papers
Comparison principles for stochastic Volterra equations
Ole Cañadas, Martin Friesen
In this work, we establish a comparison principle for stochastic Volterra equations with respect to the initial condition and the drift applicable to a wide class of Volterra k…
Regular occupation measures of Volterra processes
Martin Friesen
We introduce a local non-determinism condition for Volterra Itô processes that captures smoothing properties of possibly degenerate noise. By combining the stochastic sewing lemma…
Failure of the Markov property for stochastic Volterra equations
Martin Friesen, Stefan Gerhold, Kristof Wiedermann
Memory-driven stochastic dynamics arise naturally in many applications, and stochastic Volterra equations (SVEs) offer a flexible framework for modeling such systems. Their convolu…
Stochastic Volterra equations: failure of the time-homogeneous Markov property
Martin Friesen, Stefan Gerhold, Kristof Wiedermann
Path-dependence is a defining feature of many real-world systems, with applications ranging from population dynamics to rough volatility models and electricity spot prices. In stoc…
Limit theorems for stochastic Volterra processes
Luigi Amedeo Bianchi, Stefano Bonaccorsi, Ole Cañadas +1
We introduce an abstract Hilbert space-valued framework of Markovian lifts for stochastic Volterra equations with operator-valued Volterra kernels. Our main results address the exi…
Small-time central limit theorems for stochastic Volterra integral equations and their Markovian lifts
Martin Friesen, Stefan Gerhold, Kristof Wiedermann
We study small-time central limit theorems for stochastic Volterra integral equations with Hölder continuous coefficients and general locally square integrable Volterra kernels. W…