$\Lambda$-linked coupling for drifting Brownian motions

Motoya Machida

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arXiv · 1908.07559

$\Lambda$-linked coupling for drifting Brownian motions

Motoya Machida

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Abstract

We raise a question on whether a dynamical system driven by Markov process is Markovian, for which we are able to propose a criterion and examples of positive case. This investigation leads us to develop (i) a general construction of intertwining dual via Liggett duality, and (ii) a realization of $\Lambda$-linked coupling in a form of dynamical system. We show this construction of intertwining dual and $\Lambda$-linked coupling for an $n$-dimensional drifting Brownian motion when it is a characteristic diffusion. In particular, it includes an extension of Pitman's $2M-W$ theorem by Rogers and Pitman as a special case.

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BibTeX RIS

Motoya Machida. 2019-08-20. $\Lambda$-linked coupling for drifting Brownian motions. https://arxiv.org/abs/1908.07559

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