For regular Volterra kernels the square-root process obeys a time-dependent Feller condition and stays positive; for rough regularly-varying kernels it hits zero with positive probability and carries an atom at the boundary.
Local extinction in continuous-state branching processes with immigration
2 Pith papers cite this work. Polarity classification is still indexing.
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Sufficient conditions are given for CIMBI processes to avoid the boundary entirely and for hitting it almost surely (diffusion case) or with positive probability (finite-activity jumps) under small constant immigration.
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Boundary behaviour of the Volterra square-root process
For regular Volterra kernels the square-root process obeys a time-dependent Feller condition and stays positive; for rough regularly-varying kernels it hits zero with positive probability and carries an atom at the boundary.
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Boundary behavior of continuous-state interacting multi-type branching processes with immigration
Sufficient conditions are given for CIMBI processes to avoid the boundary entirely and for hitting it almost surely (diffusion case) or with positive probability (finite-activity jumps) under small constant immigration.