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Wiener–Hopf Factorization for Time-Inhomogeneous Markov Chains and its Application

Bielecki Tomasz R., Cialenco Igor, Gong Ruoting, Huang Yicong

Probability and Mathematical Statistics

2020

Vol. 40, Fasc. 2

225--244

We derive the Wiener–Hopf factorization for a finite-state timeinhomogeneous Markov chain. Considered as the first step in the direction of theWiener–Hopf factorization for time-inhomogeneous Markov chains, this work deals only with a special, but important class of time-inhomogeneous Markovian generators, namely piecewise constant generators, which allows us to use an appropriately tailored randomization technique.

A note on Dirichlet processes

Rozkosz A.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 3

277-286

We consider an m-symmetric conservative Hunt process (Chi, Rho[chi]) on Chi such that for some phi [belongs to] L2(Chi; my) the composite process phi(Chi) is for quasi every starting point chi [belongs to] Chi a continuous Rho[chi]-Dirichlet process in the sense of Foellmer. We show that the martingale and the zero quadratic variation parts in the decomposition od phi(Chi} can be chosen to be additive functionals and moreover, how to pass from Foellmer's decomposition to Fukushima's and the Lyons-Zheng decompositions of phi(Chi).

A representation theorem for continuous additive functionals of zero quadratic variation

Wolf J.

Probability and Mathematical Statistics

1998

Vol. 18, Fasc. 2

385--397

We study continuous additive functionals of zero quadratic variation of strong Markov continuous local martingales by means of stochastic calculus. We show that they admit a representation as a stochastic integral with respect to local time in the sense of Bouleau and Yor.