Markov-modulated affine processes

Markov-modulated Ornstein-Uhlenbeck processes

In this paper we consider an Ornstein-Uhlenbeck (ou) process (M(t))t>0 whose parameters are determined by an external Markov process (X(t))t>0 on a nite state space {1, . . . , d}; this process is usually referred to as Markov-modulated Ornstein-Uhlenbeck (or: mmou). We use stochastic integration theory to determine explicit expressions for the mean and variance of M(t). Then we establish a sys...

Skew Convolution Semigroups and Affine Markov Processes

A general affine Markov semigroup is formulated as the convolution of a homogeneous one with a skew convolution semigroup. We provide some sufficient conditions for the regularities of the homogeneous affine semigroup and the skew convolution semigroup. The corresponding affine Markov process is constructed as the strong solution of a system of stochastic equations with non-Lipschitz coefficien...

Bayesian analysis of Markov Modulated Bernoulli Processes

We consider Markov Modulated Bernoulli Processes (MMBP) where the success probability of a Bernoulli process evolves over time according to a Markov chain. The MMBP is applied in reliability modeling where systems and components function in a randomly changing environment. Some of these applications include, but are not limited to, reliability assessment in power systems that are subject to flu...

Simulating internet traffic with Markov-modulated processes

This paper considers various Markov-modulated processes which have been used in the literature to model internet traffic. In particular, such processes have been used to replicate the long-range dependent nature of internet traffic and the justification for doing so is that long-range dependence (LRD) has important effects on delays and buffer occupancy in traffic models. However, in combinatio...

The Effect of Boundary Constraints on Markov-Modulated Diffusion Processes