In this paper a relative analysis of moments reversion of the class of theta methods is provided for an stochastic differential equation with Poisson-driven jumps. We first determine under which conditions the first and second moments revert to steady state values. Second, we consider two different classes of implicit theta methods; theta-Euler method, and compensated theta-Euler method, and derive closed-form expressions for the conditional and asymptotic means and variances of considered methods. We provide a full analysis about the possibility to find methods able to replicate such long-terms quantities. Finally, to verify our theoretical results numerical experiments are given.

A long term analysis of stochastic theta methods for mean reverting linear process with jumps

D'Ambrosio R.;Moradi A.;Scalone C.
2023-01-01

Abstract

In this paper a relative analysis of moments reversion of the class of theta methods is provided for an stochastic differential equation with Poisson-driven jumps. We first determine under which conditions the first and second moments revert to steady state values. Second, we consider two different classes of implicit theta methods; theta-Euler method, and compensated theta-Euler method, and derive closed-form expressions for the conditional and asymptotic means and variances of considered methods. We provide a full analysis about the possibility to find methods able to replicate such long-terms quantities. Finally, to verify our theoretical results numerical experiments are given.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/204783
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