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Title: Bounds in total variation distance for discrete-time processes on the sequence space
Authors: Flint, Ian
Privault, Nicolas
Torrisi, Giovanni Luca
Keywords: Science::Mathematics
Issue Date: 2018
Source: Flint, I., Privault, N., & Torrisi, G.L. (2018). Bounds in total variation distance for discrete-time processes on the sequence space. Potential Analysis, 52, 223–243. doi:10.1007/s11118-018-9744-0
Journal: Potential Analysis 
Abstract: Let ℙ and ℙ~ be the laws of two discrete-time stochastic processes defined on the sequence space Sℕ, where S is a finite set of points. In this paper we derive a bound on the total variation distance d TV(ℙ, ℙ~) in terms of the cylindrical projections of ℙ and ℙ~. We apply the result to Markov chains with finite state space and random walks on ℤ with not necessarily independent increments, and we consider several examples. Our approach relies on the general framework of stochastic analysis for discrete-time obtuse random walks and the proof of our main result makes use of the predictable representation of multidimensional normal martingales. Along the way, we obtain a sufficient condition for the absolute continuity of ℙ~ with respect to ℙ which is of interest in its own right.
ISSN: 0926-2601
DOI: 10.1007/s11118-018-9744-0
Rights: This is a post-peer-review, pre-copyedit version of an article published in Potential Analysis. The final authenticated version is available online at:
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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