Feller property of regime-switching jump diffusion processes with hybrid jumps
HAP Blom (TU Delft - Air Transport & Operations)
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Abstract
The transition kernel of an ℝ
n-valued diffusion or jump diffusion process {X
t} is known to satisfy the Feller property if {X
t} is the solution of an SDE whose coefficients are Lipschitz continuous. This Lipschitz route to Feller falls short if {X
t} is the solution of an SDE whose coefficients depend on a state-dependent regime-switching process {θ
t}. In this paper it is shown that pathwise uniqueness and the Feller property are satisfied under mild conditions for a regime-switching jump diffusion process {X
t, θ
t} with hybrid jumps, i.e. jumps in {X
t} that occur simultaneously with {θ
t} switching.
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