Mathematics – Probability
Scientific paper
2011-04-06
Mathematics
Probability
69 pages
Scientific paper
Consider a system $X = ((x_\xi(t)), \xi \in \Omega_N)_{t \geq 0}$ of interacting Fleming-Viot diffusions with mutation and selection which is a strong Markov process with continuous paths and state space $(\CP(\I))^{\Omega_N}$, where $\I$ is the type space, ${\Omega_N}$ the geographic space is assumed to be a countable group and $\CP$ denotes the probability measures. We establish various duality relations for this process. These dualities are function-valued processes which are driven by a coalescing-branching random walk, that is, an evolving particle system which in addition exhibits certain changes in the function-valued part at jump times driven by mutation. In the case of a finite type space $\I$ we construct a set-valued dual process, which is a Markov jump process, which is very suitable to prove ergodic theorems which we do here. The set-valued duality contains as special case a duality relation for any finite state Markov chain. In the finitely many types case there is also a further tableau-valued dual which can be used to study the invasion of fitter types after rare mutation. This is carried out in \cite{DGsel} and \cite{DGInvasion}.
Dawson Donald A.
Greven Andreas
No associations
LandOfFree
Duality for spatially interacting Fleming-Viot processes with mutation and selection does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Duality for spatially interacting Fleming-Viot processes with mutation and selection, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Duality for spatially interacting Fleming-Viot processes with mutation and selection will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-418049