Asymptotics of Markov Kernels and the Tail Chain

An asymptotic model for the extreme behavior of certain Markov chains is the ‘tail chain’. Generally taking the form of a multiplicative random walk, it is useful in deriving extremal characteristics, such as point process limits. We place this model in a more general context, formulated in terms of extreme value theory for transition kernels, and extend it by formalizing the distinction between extreme and nonextreme states. We make the link between the update function and transition kernel forms considered in previous work, and we show that the tail chain model leads to a multivariate regular variation property of the finite-dimensional distributions under assumptions on the marginal tails alone.

Asymptotics of Markov Kernels and the Tail Chain

An asymptotic model for the extreme behavior of certain Markov chains is the ‘tail chain’. Generally taking the form of a multiplicative random walk, it is useful in deriving extremal characteristics, such as point process limits. We place this model in a more general context, formulated in terms of extreme value theory for transition kernels, and extend it by formalizing the distinction between extreme and nonextreme states. We make the link between the update function and transition kernel forms considered in previous work, and we show that the tail chain model leads to a multivariate regular variation property of the finite-dimensional distributions under assumptions on the marginal tails alone.

Threshold Values Analysis of Substrate Parameters Based on MEMS Microstrip Filter

High frequency filters are important components in microwave facilities application. With miniature volume, high performance and integratability, MEMS microstrip filter can significantly improve performance of Radio frequency system. By calculating chebyshev coupled microstrip bandpass filter design scheme, Threshold values of MEMS microstrip substrate parameters are defined to analyze dimensions variation property of MEMS microstrip filter relates with substrate parameters. Selection principle of substrate parameters for MEMS microstrip filter is presented, which indicates thickness and relative dielectric constant of substrate should not exceed the threshold values. The principle of threshold values can be applied as a guide on research and application of MEMS microstrip filter.