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.
On the boundary behavior of multi-type continuous-state branching processes with immigration
2 Pith papers cite this work. Polarity classification is still indexing.
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For regular Volterra kernels the square-root process avoids zero under a time-dependent Feller condition while rough regularly-varying kernels force an atom at zero, with the limit law still having finite negative exponential moments; equivalent martingale measures in the Volterra Heston model exist
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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.
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Boundary behaviour of the Volterra square-root process
For regular Volterra kernels the square-root process avoids zero under a time-dependent Feller condition while rough regularly-varying kernels force an atom at zero, with the limit law still having finite negative exponential moments; equivalent martingale measures in the Volterra Heston model exist