Abstract
We study a symmetric continuous time branching random walk on a d-dimensional lattice with the zero mean and a finite variance of jumps under the assumption that the birth and the death of particles occur at a single lattice point. In the critical and subcritical cases the asymptotic behavior of the survival probability of particles on Z d at time t, as t → ∞, is obtained. Conditional limit theorems for the population size are proved. The models of a branching random walk in a spatially inhomogeneous medium could be applied to the study of the long-time behavior of objects in a catalytic environment.
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This work is supported by the RFBR grant 07-01-00362.
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Yarovaya, E. (2010). Critical and Subcritical Branching Symmetric Random Walks on d-Dimensional Lattices. In: Skiadas, C. (eds) Advances in Data Analysis. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4799-5_15
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DOI: https://doi.org/10.1007/978-0-8176-4799-5_15
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