Strong Stationary Duality for Diffusion Processes

Preprint English OPEN
Fill, James Allen; Lyzinski, Vince;
(2014)
  • Subject: Mathematics - Probability

We develop the theory of strong stationary duality for diffusion processes on compact intervals. We analytically derive the generator and boundary behavior of the dual process and recover a central tenet of the classical Markov chain theory in the diffusion setting by l... View more
  • References (26)
    26 references, page 1 of 3

    [S(x) − S(η)] M (dη), Σ(l) := [M (x) − M (η)] dS(η) π(y) Π(x) −1 M (y) M (y) s(y) dy. s(y)M (y) dy − s(y)M (y) dy < ∞ − M (y) dy s(y)[M (y) − M (x)] dy = Σ(1) = ∞ s(y) M (y) − M (1) s(y)[M (1) − M (y)] dy = N (1) < ∞. A − α A − Proof. Let f ∈ F [0, 1]. By Remark 3.12, we have for all t > 0 that (Πt, f ) = (Πt∗, Λf ). Therefore, writing Rt = dΠt/dΠ as usual, we have Z Z 1 + c2λn,1tn

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    [14] JamesAllen Fill and Vince Lyzinski. Hitting times and interlacing eigenvalues: A stochastic approach using intertwinings. Journal of Theoretical Probability, pages 1-28, 2012.

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