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Fast Adaptive Uniformization for the Chemical Master Equation

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A higher-order numerical framework for stochastic simulation of chemical reaction systems

Background: In this paper, we present a framework for improving the accuracy of fixed-step methods for Monte Carlo simulation of discrete stochastic chemical kinetics. Stochasticity is ubiquitous in many areas of cell biology, for example in gene regulatio ...

Biomed Central Ltd2012

Affine Variance Swap Curve Models

Damir Filipovic

This paper provides a brief overview of the stochastic modeling of variance swap curves. Focus is on affine factor models. We propose a novel drift parametrization which assures that the components of the state process can be matched with any pre-specified ...

2012

Propagation Models for Biochemical Reaction Networks

Maria-Emanuela-Canini Mateescu

In this thesis we investigate different ways of approximating the solution of the chemical master equation (CME). The CME is a system of differential equations that models the stochastic transient behaviour of biochemical reaction networks. It does so by d ...

EPFL2011

Stochastic integrals for spde's: A comparison

Robert Dalang

We present the Walsh theory of stochastic integrals with respect to martingale measures, and various extensions of this theory, alongside of the Da Prato and Zabczyk theory of stochastic integrals with respect to Hilbert-space-valued Wiener processes, and ...

Elsevier2011

Fast adaptive uniformisation of the chemical master equation

Maria-Emanuela-Canini Mateescu, Verena Wolf

Within systems biology there is an increasing interest in the stochastic behaviour of biochemical reaction networks. An appropriate stochastic description is provided by the chemical master equation, which represents a continuous-time Markov chain (CTMC). ...

2010

Hybrid Numerical Solution of the Chemical Master Equation

Maria-Emanuela-Canini Mateescu, Verena Wolf

We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is based on the const ...

2010

Macroscopic stability for nonfinite range kernels

Thomas Mountford

We extend the strong macroscopic stability introduced in Bramson and Mountford [Ann. Probab. 30 (2002) 1082-1130] for one-dimensional asymmetric exclusion processes with finite range to a large class of one-dimensional conservative attractive models (inclu ...

2010

Sliding Window Abstraction for Infinite Markov Chains

Maria-Emanuela-Canini Mateescu, Verena Wolf

We present an on-the-fly abstraction technique for infinite-state continuous-time Markov chains. We consider Markov chains that are specified by a finite set of transition classes. Such models naturally represent biochemical reactions and therefore play an ...

2009

Implicit methods for modeling gene regulatory networks

Abhishek Garg

Advancements in high-throughput technologies to measure increasingly complex biological phenomena at the genomic level are rapidly changing the face of biological research from single-gene single-protein experimental approach to studying the behaviour of a ...

EPFL2009

Stochastic Modeling and Control of Biological Systems: The Lactose Regulation System of Escherichia coli

Mahmut Selman Sakar

In this paper, we present a comprehensive framework for stochastic modeling, model abstraction, and controller design for a biological system. The first half of the paper concerns modeling and model abstraction of the system. Most models in systems biology ...

Institute of Electrical and Electronics Engineers2008