Approximation of Invariant Measures for Regime-switching Diffusions
By Jianhai Bao, Jinghai Shao, Chenggui Yuan. Potential Analysis, 2014
49 citations recorded by the source corpus.
In this paper, we are concerned with long-time behavior of Euler-Maruyama schemes associated with regime-switching diffusion processes. The key contributions of this paper lie in that existence and uniqueness of numerical invariant measures are addressed (i) for regime-switching diffusion processes with finite state spaces by the Perron-Frobenius theorem if the “averaging condition” holds, and, for the case of reversible Markov chain, via the principal eigenvalue approach provided that the principal eigenvalue is positive; (ii) for regime-switching diffusion processes with countable state spaces by means of a finite partition method and an M-Matrix theory. We also reveal that numerical invariant measures converge in the Wasserstein metric to the underlying ones. Several examples are constructed to demonstrate our theory.
Subfields: Finance, Modeling and Simulation, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/c250c6f6a7f655db94187dad5ff1d7f7bff667eb
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Finance
In Modeling and Simulation
In Statistics and Probability
Citations in the corpus
- Certain properties related to well posedness of switching diffusions (2017, background): “Suppose that the switching process α(t) has generator Q = ( −f(x) f(x) 0 0 ) , where f(x) is a smooth positive function with compact support and f(x) = x for x ∈ [1, 2].”
- Explicit numerical approximations for stochastic differential equations in finite and infinite horizons: truncation methods, convergence in pth moment, and stability (2019, methodology): “Explicit Euler–Maruyama (EM) schemes are most popular for approximating the solutions of SDEs under global Lipschitz continuously; see, for example, Kloeden & Platen (1992) and Higham et al. (2002). However, many important SDE models satisfy only local Lipschitz conditions or have growth rates faste”