6 papers
On a class of constrained Bayesian filters and their numerical implementation in high-dimensional state-space Markov models
Utku Erdogan, Gabriel J. Lord, Joaquin Miguez
Bayesian filtering is a key tool in many problems that involve the online processing of data, including data assimilation, optimal control, nonlinear tracking and others. Unfortuna…
Preserving invariant domains and strong approximation of stochastic differential equations
Utku Erdogan, Gabriel Lord
In this paper, we develop numerical methods for solving Stochastic Differential Equations (SDEs) with solutions that evolve within a hypercube in . Our approach i…
Strong Convergence of a Splitting Method for the Stochastic Complex Ginzburg-Landau Equation
Marvin Jans, Gabriel J. Lord, Mariya Ptashnyk
We consider the numerical approximation of the stochastic complex Ginzburg-Landau equation with additive noise on the one dimensional torus. The complex nature of the equation mean…
Numerical approximation of SDEs driven by fractional Brownian motion for all using WIS integration
Utku Erdogan, Gabriel J. Lord, Roy B. Schieven
We examine the numerical approximation of a quasilinear stochastic differential equation (SDE) with multiplicative fractional Brownian motion. The stochastic integral is interprete…
Strong convergence of a class of adaptive numerical methods for SDEs with jumps
Cónall Kelly, Gabriel Lord, Fandi Sun
We develop adaptive time-stepping strategies for Itô-type stochastic differential equations (SDEs) with jump perturbations. Our approach builds on adaptive strategies for SDEs. Ada…
Strong Convergence of a GBM Based Tamed Integrator for SDEs and an Adaptive Implementation
Utku Erdogan, Gabriel J. Lord
We introduce a tamed exponential time integrator which exploits linear terms in both the drift and diffusion for Stochastic Differential Equations (SDEs) with a one sided globally…