Related papers: The randomized Milstein scheme for stochastic Volt…
We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have very rough sample paths. The main results obtained in…
In the present paper we consider the regularizing properties of the repeated midpoint rule for the stable solution of weakly singular Volterra integral equations of the first kind with perturbed right hand sides. The H\"older continuity of…
In this paper we study set-valued Volterra-type stochastic integrals driven by L\'{e}vy processes. Upon extending the classical definitions of set-valued stochastic integral functionals to convoluted integrals with square-integrable…
We introduce the Volterra Stein-Stein model with stochastic interest rates, where both volatility and interest rates are driven by correlated Gaussian Volterra processes. This framework unifies various well-known Markovian and non-Markovian…
In the present paper we investigate the performance of explicit splitting schemes and related techniques applied to a rigid body model subject to a stochastic torque and random perturbations in the inertia tensor. Results are discussed and…
In usual stochastic volatility models, the process driving the volatility of the asset price evolves according to an autonomous one-dimensional stochastic differential equation. We assume that the coefficients of this equation are smooth.…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
Volterra processes appear in several applications ranging from turbulence to energy finance where they are used in the modelling of e.g. temperatures and wind and the related financial derivatives. Volterra processes are in general…
The Volterra integral-functional series is the classic approach for nonlinear black box dynamical systems modeling. It is widely employed in many domains including radiophysics, aerodynamics, electronic and electrical engineering and many…
The pseudo-marginal algorithm is a popular variant of the Metropolis--Hastings scheme which allows us to sample asymptotically from a target probability density $\pi$, when we are only able to estimate an unnormalized version of $\pi$…
We introduce a novel and efficient simulation scheme for Hawkes processes on a fixed time grid, leveraging their affine Volterra structure. The key idea is to first simulate the integrated intensity and the counting process using Inverse…
We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…
This article studies an infinite dimensional analog of Milstein's scheme for finite dimensional stochastic ordinary differential equations (SODEs). The Milstein scheme is known to be impressively efficient for SODEs which fulfill a certain…
We present an abstract concept for the error analysis of numerical schemes for semilinear stochastic partial differential equations (SPDEs) and demonstrate its usefulness by proving the strong convergence of a Milstein-Galerkin finite…
We study the weak convergence of iterates of so-called centred kernel quadratic stochastic operators. These iterations, in a population evolution setting, describe the additive perturbation of the arithmetic mean of the traits of an…
We investigate the well-posedness of stochastic differential equations driven by fractional Brownian motion, focusing on the long-range dependent case $H \in (\frac{1}{2}, 1)$. While existing results on regularization by such noise…
We consider a process $X^\ve$ that solves a stochastic Volterra equation with an unknown parameter $\theta^\star$ in the drift function. The Volterra kernel is singular, and includes as an example, $K\_0(u)=c u^{\alpha-1/2} \id{u>0}$ with…
The Ensemble Kalman methodology in an inverse problems setting can be viewed as an iterative scheme, which is a weakly tamed discretization scheme for a certain stochastic differential equation (SDE). Assuming a suitable approximation…
Previously, the authors derived an analog of the Euler-Maru\-yama method (fEMM) for free stochastic differential equations (fSDEs) and proved strong convergence of order $\gamma=0.5$ in $L_1(\varphi)$-norm under certain assumptions. In this…
The aim of this note is to propose a novel numerical scheme for drift-less one dimensional stochastic differential equations of It\^o's type driven by standard Brownian motion. Our approximation method is equivalent to the well known…