1. A long term analysis of stochastic theta methods for mean reverting linear process with jumps.
- Author
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D'Ambrosio, Raffaele, Moradi, Afsaneh, and Scalone, Carmela
- Subjects
- *
STOCHASTIC analysis , *JUMP processes , *STOCHASTIC differential equations , *MOMENTS method (Statistics) , *THETA functions - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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