Convergence of a discretization scheme for jump-diffusion processes with state–dependent intensities

This paper proves a convergence result for a discretization scheme for simulating jump–diffusion processes with state–dependent jump intensities. With a bound on the intensity, the point process of jump times can be constructed by thinning a Poisson random measure using state–dependent thinning probabilities. Between the jump epochs of the Poisson random measure, the dynamics of the constructed process are purely diffusive and may be simulated using standard discretization methods. Under conditions on the coefficient functions of the jump–diffusion process, we show that the weak convergence order of this method equals the weak convergence order of the scheme used for the purely diffusive intervals: the construction of jumps does not degrade the convergence of the method.

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