Abhishek Pal Majumder: Long time asymptotics of some stochastic reaction networks
Time: Wed 2017-10-04 15.15 - 16.15
Location: Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University
Participating: Abhishek Pal Majumder (SU)
Abstract: We consider modelling a network of species whose evolutions (birth, death, conversion) depend on presence of species counts of another reaction network (called host) that is assumed to be ergodic. These models are helpful in explaining various long term aspects of gene regulatory networks. We studied the joint distribution of the species of interest (called parasites) in a finite time horizon along with analyzing the ergodicity conditions. Under those conditions the equilibrium distribution of the parasite species is found to be a mixture of Poissons. The mixing measure can be uniquely identified as the law of the fixed point of a stochastic recurrence equation (of type \(X = AX +B\) in law) where A and B are certain path-wise integral type functionals derived from the stochastic dynamics of the host reaction network.
A joint work with Carsten Wiuf, Daniele Cappelletti