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Search: MSC category 60J25 ( Continuous-time Markov processes on general state spaces )

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1. CJM 2015 (vol 68 pp. 129)

Shiozawa, Yuichi
Lower Escape Rate of Symmetric Jump-diffusion Processes
We establish an integral test on the lower escape rate of symmetric jump-diffusion processes generated by regular Dirichlet forms. Using this test, we can find the speed of particles escaping to infinity. We apply this test to symmetric jump processes of variable order. We also derive the upper and lower escape rates of time changed processes by using those of underlying processes.

Keywords:lower escape rate, Dirichlet form, Markov process, time change
Categories:60G17, 31C25, 60J25

2. CJM 2003 (vol 55 pp. 3)

Baake, Michael; Baake, Ellen
An Exactly Solved Model for Mutation, Recombination and Selection
It is well known that rather general mutation-recombination models can be solved algorithmically (though not in closed form) by means of Haldane linearization. The price to be paid is that one has to work with a multiple tensor product of the state space one started from. Here, we present a relevant subclass of such models, in continuous time, with independent mutation events at the sites, and crossover events between them. It admits a closed solution of the corresponding differential equation on the basis of the original state space, and also closed expressions for the linkage disequilibria, derived by means of M\"obius inversion. As an extra benefit, the approach can be extended to a model with selection of additive type across sites. We also derive a necessary and sufficient criterion for the mean fitness to be a Lyapunov function and determine the asymptotic behaviour of the solutions.

Keywords:population genetics, recombination, nonlinear $\ODE$s, measure-valued dynamical systems, Möbius inversion
Categories:92D10, 34L30, 37N30, 06A07, 60J25

3. CJM 2000 (vol 52 pp. 92)

Dhersin, Jean-Stéphane; Serlet, Laurent
A Stochastic Calculus Approach for the Brownian Snake
We study the ``Brownian snake'' introduced by Le Gall, and also studied by Dynkin, Kuznetsov, Watanabe. We prove that It\^o's formula holds for a wide class of functionals. As a consequence, we give a new proof of the connections between the Brownian snake and super-Brownian motion. We also give a new definition of the Brownian snake as the solution of a well-posed martingale problem. Finally, we construct a modified Brownian snake whose lifetime is driven by a path-dependent stochastic equation. This process gives a representation of some super-processes.

Categories:60J25, 60G44, 60J80, 60J60

4. CJM 1997 (vol 49 pp. 24)

Bertoin, Jean; Le Gall, Jean-François; Le Jan, Yves
Spatial branching processes and subordination
We present a subordination theory for spatial branching processes. This theory is developed in three different settings, first for branching Markov processes, then for superprocesses and finally for the path-valued process called the {\it Brownian snake}. As a common feature of these three situations, subordination can be used to generate new branching mechanisms. As an application, we investigate the compact support property for superprocesses with a general branching mechanism.

Categories:60J80, 60J25, 60J27, 60J55, 60G57

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