Abstract Consider a Lamperti–Kiu Markov additive process $(J, \xi)$ on $\{+, -\}\times\mathbb R\cup \{-\infty\}$ , where J is the modulating chain component. First we study finiteness of exponential functional and then consider its moments tail asymptotics under Cramér’s condition. In strong subexponential case determine tails some further assumptions.

In this work, we introduce a hidden Markov field model for wavelet image coefficients within a subband and apply it to the image denoising problem. Specifically, we propose to model wavelet image coefficients within subbands as Gaussian random variables with parameters determined by the underlying hidden Markov process. Our model is inspired by the recent Estimation-Quantization (EQ) image code...

This paper studies additive subordination, which we show is a useful technique for constructing time-inhomogeneous Markov processes with analytical tractability. This technique is a natural generalization of Bochner’s subordination that has proven to be extremely useful in financial modelling. Probabilistically, Bochner’s subordination corresponds to a stochastic time change with respect to an ...