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SUMMARY:Subexponential lower bounds for f-ergodic Markov processes - Miha 
 Bresar (University of Warwick)
DTSTART:20241202T140000Z
DTEND:20241202T150000Z
UID:TALK223786@talks.cam.ac.uk
DESCRIPTION:In this talk I will describe a criterion for establishing lowe
 r bounds on the rate of convergence in f-variation of a continuous-time er
 godic Markov process to its invariant measure. The criterion consists of n
 ovel super- and submartingale conditions for certain functionals of the Ma
 rkov process. It provides a general approach for proving lower bounds on t
 he tails of the invariant measure and the rate of convergence in f-variati
 on of a Markov process\, analogous to the widely used Lyapunov drift condi
 tions for upper bounds. Our key technical innovation\, which will be discu
 ssed in the talk\, produces lower bounds on the tails of the heights and d
 urations of the excursions from bounded sets of a continuous-time Markov p
 rocess using path-wise arguments.\nI will present applications of our theo
 ry to elliptic diffusions and Levy-driven stochastic differential equation
 s with known polynomial/stretched exponential upper bounds on their rates 
 of convergence. Our lower bounds match asymptotically the known upper boun
 ds for these classes of models\, thus establishing their rate of convergen
 ce to stationarity. The generality of our approach suggests that analogous
  to the Lyapunov drift conditions for upper bounds\, our methods can be ex
 pected to find applications in many other settings. This is joint work wit
 h Aleksandar Mijatovic at Warwick.
LOCATION:Seminar Room 2\, Newton Institute
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