44 citations · 60 across the 6 of their papers we have counts for
6 papers
Strong Error Analysis of the -Method for Stochastic Hybrid Systems
Martin G. Riedler, Girolama Notarangelo
We discuss numerical approximation methods for Random Time Change equations which possess a deterministic drift part and jump with state-dependent rates. It is first established th…
Spatio-Temporal Hybrid (PDMP) Models: Central Limit Theorem and Langevin Approximation for Global Fluctuations. Application to Electrophysiology
Martin G Riedler, Michele Thieullen
In the present work we derive a Central Limit Theorem for sequences of Hilbert-valued Piecewise Deterministic Markov process models and their global fluctuations around their deter…
Large Deviations for Nonlocal Stochastic Neural Fields
Christian Kuehn, Martin G. Riedler
We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a -Wiener process and focus on nois…
Laws of large numbers and Langevin approximations for stochastic neural field equations
Evelyn Buckwar, Martin G. Riedler
In this study we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson-Cowan equation can be obtained as the limit in probability on c…
Almost sure convergence of numerical approximations for Piecewise Deterministic Markov Processes
Martin G. Riedler
Hybrid systems, and Piecewise Deterministic Markov Processes in particular, are widely used to model and numerically study systems exhibiting multiple time scales in biochemical re…
Limit theorems for infinite-dimensional piecewise deterministic Markov processes. Applications to stochastic excitable membrane models
Martin G. Riedler, Michèle Thieullen, Gilles Wainrib
We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous…