Quasi-ergodicity for absorbing Markov processes via deviation inequality
Chen, Jinwen1 ; Jian, Siqi2
1 Department of Mathematics,Tsinghua University, Beijing, P. R. China.
2 School of Statistics, Capital University of Economics and Business, Beijing, P. R. China
ESAIM: Probability and Statistics, Tome 21 (2017), pp. 159-167.

In this note, taking the killed Brownian motion as an illustrative model, we derive a conditional deviation inequality for ∫ 0 t V(X s )ds for certain (unbounded) functions V. Then we apply it to prove a quasi L 1 -ergodic theorem for the killed process.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2017009
Classification : 60J65, 60F99, 28Dxx
Mots clés : Absorbing Markov process, deviation inequality, quasi-ergodicity
Chen, Jinwen 1 ; Jian, Siqi 2

1 Department of Mathematics,Tsinghua University, Beijing, P. R. China.
2 School of Statistics, Capital University of Economics and Business, Beijing, P. R. China 
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     author = {Chen, Jinwen and Jian, Siqi},
     title = {Quasi-ergodicity for absorbing {Markov} processes via deviation inequality},
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     pages = {159--167},
     publisher = {EDP-Sciences},
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Chen, Jinwen; Jian, Siqi. Quasi-ergodicity for absorbing Markov processes via deviation inequality. ESAIM: Probability and Statistics, Tome 21 (2017), pp. 159-167. doi : 10.1051/ps/2017009. http://www.numdam.org/articles/10.1051/ps/2017009/

L.A. Breyer and G.O. Roberts, A quasi-ergodic theorem for evanescent processes. Stochastic Processes Appl. 84 (1999) 177–186. | DOI | MR | Zbl

J.W. Chen and S.Q. Jian, Some limit theorems of killed Brownian motion, Sci. China Math. 56 (2013) 497–514. | DOI | MR | Zbl

J.W. Chen, H.T. Li and S.Q. Jian, Some limit theorems for absorbing Markov processes. J. Phys. A: Math. Theor. 45 (2012) 345–003. | MR | Zbl

K.L. Chung and Z.X. Zhao, From Brownian motion to Schrodinger’s equation. Springer, Berlin (1995). | MR | Zbl

J.D. Deuschel and D.W. Stroock, Large Deviations. Academic Press, Boston (1989). | MR | Zbl

L.C. Evans, Partial Differential Equations. American Mathematical society (1998). | MR | Zbl

S.C. Port and C.J. Stone, Brownian motion and classical potential theory. Academic Press, Inc (1978). | MR | Zbl

L. Wu, A deviation inequality for non-reversible Markov processes. Ann. Inst. Henri Poincaré. Prob. Stat. 11 (2000) 435–445. | DOI | Numdam | MR | Zbl

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