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BEGIN:VEVENT
DTSTAMP:20241125T092519Z
DTSTART:20241204T150000Z
DTEND:20241204T163000Z
SUMMARY:Probability Seminar: Goran Peskir (University Of Manchester) - Th
 e Gapeev-Shiryaev Conjecture.
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}a180-m3wtoc
 fj-7cgzvp
DESCRIPTION:Goran Peskir will speak at the Probability seminar.\n\nTitle:
  The Gapeev-Shiryaev Conjecture\n\nSpeaker: Goran Peskir\n\nAbstract: Th
 e Gapeev-Shiryaev conjecture can be broadly stated as follows: `Monotoni
 city of the signal-to-noise ratio implies monotonicity of the optimal st
 opping boundaries'. The conjecture was originally formulated both within
  (i) sequential testing problems for diffusion processes (where one need
 s to decide which of the two drifts is being indirectly observed) and (i
 i) quickest detection problems for diffusion processes (where one needs 
 to detect when the initial drift changes to a new drift). In this talk w
 e present proofs of the Gapeev-Shiryaev conjecture both in (i) the seque
 ntial testing setting (under Lipschitz/Holder coefficients of the underl
 ying SDEs) and (ii) the quickest detection setting (under analytic coeff
 icients of the underlying SDEs). The method of proof in the sequential t
 esting setting relies upon a stochastic time change and pathwise compari
 son arguments. Both arguments break down in the quickest detection setti
 ng and get replaced by arguments arising from a stochastic maximum princ
 iple for hypoelliptic equations (satisfying Hormander's condition) that 
 is of independent interest. Verification of the Gapeev-Shiryaev conjectu
 re establishes the fact that sequential testing and quickest detection p
 roblems with monotone signal-to-noise ratios are amenable to known metho
 ds of solution. [This is joint work with P. A. Ernst.]\n
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 2\, Alan Turing Building\, Manchester
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