On Adjoint Additive Processes

Kristian P. Evans; Niels Jacob

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arXiv · 1901.03529

On Adjoint Additive Processes

Kristian P. Evans·Niels Jacob

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Abstract

Starting with an additive process $(Y_t)_{t\geq0}$, it is in certain cases possible to construct an adjoint process $(X_t)_{t\geq0}$ which is itself additive. Moreover, assuming that the transition densities of $(Y_t)_{t\geq0}$ are controlled by a natural pair of metrics $\mathrm{d}_{ψ,t}$ and $δ_{ψ,t}$, we can prove that the transition densities of $(X_t)_{t\geq0}$ are controlled by the metrics $δ_{ψ,1/t}$ replacing $\mathrm{d}_{ψ,t}$ and $\mathrm{d}_{ψ,1/t}$ replacing $δ_{ψ,t}$.

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BibTeX RIS

Kristian P. Evans, Niels Jacob. 2019-01-11. On Adjoint Additive Processes. https://arxiv.org/abs/1901.03529

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