Evolution of coagulation-fragmentation stochastic processes using accurate chemical master equation approach

Accurate Chemical Master Equation Solution Using Multi-Finite Buffers

The discrete chemical master equation (dCME) provides a fundamental framework for studying stochasticity in mesoscopic networks. Because of the multi-scale nature of many networks where reaction rates have large disparity, directly solving dCMEs is intractable due to the exploding size of the state space. It is important to truncate the state space effectively with quantified errors, so accurat...

Stochastic Hybrid System for Chemical Master Equation

The Coagulation - Fragmentation Equation and Its Stochastic Counterpart

We consider a coagulation multiple-fragmentation equation, which describes the concentration ct(x) of particles of mass x ∈ (0,∞) at the instant t ≥ 0 in a model where fragmentation and coalescence phenomena occur. We study the existence and uniqueness of measured-valued solutions to this equation for homogeneous-like kernels of homogeneity parameter λ ∈ (0, 1] and bounded fragmentation kernels...

Modelling Genetic Variations using Fragmentation-Coagulation Processes

We propose a novel class of Bayesian nonparametric models for sequential data called fragmentation-coagulation processes (FCPs). FCPs model a set of sequences using a partition-valued Markov process which evolves by splitting and merging clusters. An FCP is exchangeable, projective, stationary and reversible, and its equilibrium distributions are given by the Chinese restaurant process. As oppo...

Coagulation-fragmentation Processes

We study the well-posedness of coagulation-fragmentation models with diiusion for large systems of particles. The continuous and the discrete case are considered simultaneously. In the discrete situation we are concerned with a countable system of coupled reaction-diiusion equations, whereas the continuous case amounts to an uncountable system of such equations. These problems can be handled by...