Ergodicity and exponential β-mixing bounds for multidimensional diffusions with jumps

By Hiroki Masuda. 2007

174 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0c4f5f526747f707f62ba6c55deed3b97d62a8d1

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In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Exponential ergodicity of the solutions to SDE's with a jump noise (2007, background): “m)-differentiable, then F ∈ Wp,loc(R m,Rm) and ∇F coincides with its Sobolev derivative.”
Convergence of Gaussian quasi-likelihood random fields for ergodic Lévy driven SDE observed at high frequency (2013, methodology): “3(i), one can refer to Kulik [19] and Masuda [28, 29]; in this case, we may set φ(x) = |x|q outside a sufficiently large neighborhood of the origin.”
Statistical inference for time-changed Lévy processes via composite characteristic function estimation (2010, background): “Additionally, if 2κη > ζ 2 and Z0 has Gamma distribution, then Zt is stationary and exponentially α-mixing [see, e.g., Masuda (2007)].”
Criteria for ergodicity of Lévy type operators in dimension one (2008, background): “In fact, the results in [19] can be improved by our method.”
Quasi-likelihood analysis for the stochastic differential equation with jumps (2011, background): “as T →∞ forany π-integrablefunction f .Fortheexponentialmixingproperty[H2] of a jump diffusion process and the following condition [H3], we refer the reader to Masuda (2007, 2008) .”
Approximate self-weighted LAD estimation of discretely observed ergodic Ornstein-Uhlenbeck processes (2010, background): “We refer to Masuda [22] for more detailed information and history about general Lévy driven OU processes.”
Estimation of continuous-time stochastic volatility models with jumps using high-frequency data (2009, unknown): “Then if T → ∞, δ → 0 and Tδ1−² → 0 for some ² > 0 2See also Masuda (2007) (and references therein) for bounds of mixing coefficients of general jump-diffusion processes.”
Ergodicity of stochastic differential equations with jumps and singular coefficients (2017, background): “In [29] and [30], they introduced some abstract conditions for the ergodicity.”