13 citations · 30 across the 14 of their papers we have counts for
6 papers · 1 filter
On convergence of forecasts in prediction markets
Nina Badulina, Dmitry Shatilovich, Mikhail Zhitlukhin
We propose a dynamic model of a prediction market in which agents predict the values of a sequence of random vectors. The main result shows that if there are agents who make correc…
A sequential test for the drift of a Brownian motion with a possibility to change a decision
Mikhail Zhitlukhin
We construct a Bayesian sequential test of two simple hypotheses about the value of the unobservable drift coefficient of a Brownian motion, with a possibility to change the initia…
Sequential tracking of an unobservable two-state Markov process under Brownian noise
Alexey Muravlev, Mikhail Urusov, Mikhail Zhitlukhin
We consider an optimal control problem, where a Brownian motion with drift is sequentially observed, and the sign of the drift coefficient changes at jump times of a symmetric two-…
On the maximum of discretely sampled fractional Brownian motion with small Hurst parameter
Konstantin Borovkov, Mikhail Zhitlukhin
We show that the distribution of the maximum of the fractional Brownian motion with Hurst parameter over an -point set can be approximated by the…
New and refined bounds for expected maxima of fractional Brownian motion
Konstantin Borovkov, Yuliya Mishura, Alexander Novikov +1
For the fractional Brownian motion with the Hurst parameter value in (0,1/2), we derive new upper and lower bounds for the difference between the expectations of the maxi…
Bounds for expected maxima of Gaussian processes and their discrete approximations
Konstantin Borovkov, Yuliya Mishura, Alexander Novikov +1
The paper deals with the expected maxima of continuous Gaussian processes that are Hölder continuous in -norm and/or satisfy the opposite inequality for t…