We prove the Wiener-Hopf factorization for Markov Additive processes. We derive also Spitzer-Rogozin theorem for this class of processes which serves for obtaining Kendall’s formula and Fristedt representation of the cumulant matrix of the ladder epoch process. Finally, we also obtain the so-called ballot theorem.

Prospect theory assumes nonadditive decision weights for preferences over risky gambles. Such decision weights generalize additive probabilities. This article proposes a decomposition of decision weights into a component reflecting risk attitude and a new component depending on belief. The decomposition is based on an observable preference condition and does not use other empirical primitives s...

This paper introduces a class ofrobust lag-ksmoothersbased on simple low order Markov models for the Gaussian trend-like component of signal plus nonGaussian noise models. The kth order Markov models are of the kth difference form AkX t = €t where Llxt = Xt Xt-l and €t is a zero-mean white Gaussian noise process with variance <1;. The nominal additive noise is a zero-mean white Gaussian noise s...

Let {(Xn, Sn) : n = 0, 1, . . .} be a Markov additive process, where {Xn} is a Markov chain on a general state space and Sn is an additive component on R . We consider P {Sn ∈ A/ , some n} as → 0, where A ⊂ R is open and the mean drift of {Sn} is away from A. Our main objective is to study the simulation of P {Sn ∈ A/ , some n} using the Monte Carlo technique of importance sampling. If the set ...

General additive functions called rewards are defined on a "regular" finite-state Markov-renewal process. The asymptotic form of the mean total reward in [0,t] has previously been obtained, and it is known that the total rewards are joint-normally distributed as t -► oo. This paper finds the dominant asymptotic term in the covariance of the total rewetrds as a simple function of the moments of ...

Abstract. A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process (K(t), i(t), Y (t)) on (T × {1, 2} × R), where T is the twodimensional torus. Here (K(t), i(t)) is an autonomous reversible jump process, with waiting times between two jumps with finite expectation value but infinite variance. Y (t) is an additive functional of K, define...