About the Laboratory
In February-March 2014, HSE launched six new international laboratories following a tender of three-year projects headed by leading international researchers. One of the projects that received approval was the Laboratory of Stochastic Analysis and its Applications, led by Professor Valentin Konakov.
The international laboratory’s team includes a group from HSE (V. Konakov and V. Panov) and four internationally recognized professors (S. Molchanov, S. Menozzi, D. Belomestny, and A. Veretennikov). Although the researchers come from different schools in Germany, France, the UK and Russia, they share common research interests and enjoy a long history of collaboration. Several of their joint publications can be found on the Laboratory’s website.
The general aim of the Laboratory is to contribute to the theoretical underpinnings of stochastic analysis and develop practical methods for different stochastic models. The laboratory also seeks to serve as a platform for sharing knowledge by leading international researchers.
Head of Laboratory: Valentin Konakov
Academic Supervisor: Stanislav Molchanov
Project: Probabilistic and statistical methods for complex models given by stochastic differential and difference equations.
Aims of the research:
1. Statistical inference in semi- and nonparametric models.
The main aim of this part of the project is to develop statistical procedures which can be practically used for statistical inference in complex models. To a large extent theoretical research will be concentrated on the optimal rates of convergence. Moreover, we aim to develop an asymptotic distribution theory, which allows the construction of asymptotically valid confidence regions as well as the calculation of critical values and asymptotic power functions for tests based on the estimators.
2. Discretization of stochastic differential equations.
The aim of this research is to prove the local limit theorems for a wide class of discretization schemes including the classical schemes (Euler scheme, Milshtein scheme, higher order stochastic Taylor expansion schemes). It is planned to consider stochastic equations with unbounded drift and degenerate stochastic differential equations. Possible tools are the Malliavin calculus and the parametrix method for Markov chains and diffusions.
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