Multivariate COGARCH(1, 1) processes

Multivariate COGARCH(1,1) processes

Multivariate COGARCH(1,1) processes are introduced as a continuous-time models for multidimensional heteroskedastic observations. Our model is driven by a single multivariate Lévy process and the latent timevarying covariance matrix is directly specified as a stochastic process in the positive semidefinite matrices. After defining the COGARCH(1,1) process, we analyze its probabilistic propertie...

Multivariate Ecogarch Processes

A multivariate extension of the exponential continuous time GARCH(p, q) model (ECOGARCH) is introduced and studied. Stationarity and mixing properties of the new stochastic volatility model are investigated and ways to model a component-wise leverage effect are presented. AMS Subject Classification 2000: Primary: 60G51; 60H10 Secondary: 91B72; 91B84

Multivariate kernel partition processes

This article considers the problem of accounting for unknown multivariate mixture distributions within Bayesian hierarchical models motivated by functional data analysis. Most nonparametric Bayes methods rely on global partitioning, with subjects assigned to a single cluster index for all their random effects. We propose a multivariate kernel partition process (KPP) that instead allows the clus...

COVARIANCE MATRIX OF MULTIVARIATE REWARD PROCESSES WITH NONLINEAR REWARD FUNCTIONS

Multivariate reward processes with reward functions of constant rates, defined on a semi-Markov process, first were studied by Masuda and Sumita, 1991. Reward processes with nonlinear reward functions were introduced in Soltani, 1996. In this work we study a multivariate process , , where are reward processes with nonlinear reward functions respectively. The Laplace transform of the covar...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions