Stochastic geometry, stochastic analysis and spatial statistics












            ******************************************************************************************

            * Stochastic geometry, stochastic analysis and spatial statistics
            ******************************************************************************************
            The beginning of research in stochastic geometry at the Faculty goes back to the nineties,

            stochastic analysis to the seventies (Petr Mandl) of the 20th century. Since those days pa
            in these fields take place.


            Since 2019, the standard project „New approaches to modeling and statistics of random sets
            GAČR and headed by Lev Klebanov [ URL "https://www.mff.cuni.cz/en/faculty/organizational-s
            hdl=2673"] . The three year international German-Czech project „Parametric representation 

            modeling of grain microstructures in polycrystalline materials using random marked tessell
            Beneš [ URL "http://www.karlin.mff.cuni.cz/~benesv/"] , since 2017) presents cooperation b

            mathematicians and physicists from both countries, based on stochastic geometry. In both p
            Pawlas [ URL "http://www.karlin.mff.cuni.cz/~pawlas/"] takes part as an expert in spatial 
            statistics. As a theoretical basis for stochastic geometry, formulas of integral geometry 

            and extended far beyond the classical smooth setting (Jan Rataj [ URL "http://www.karlin.m
            ~rataj/"] , standard project GAČR „Generalized convexity in geometry and analysis“, since 
            Maslowski [ URL "http://www.karlin.mff.cuni.cz/~maslow/"] is working in the field of stoch

            equations and stochastic control theory. Since 2019 the standard project „Stochastic evolu
            and space-time systems", funded by GAČR is being solved together with ÚTIA AVČR.




            ******************************************************************************************

            * Selected outputs
            ******************************************************************************************
            • P. Čoupek and B. Maslowski (2017): Stochastic Evolution Equations with Volterra noise [ 

              www.sciencedirect.com/science/article/pii/S0304414916300990?via%3Dihub"] , Stoch. Proc. 
              877-900.
            • B. Kriesche, A. Koubek, Z. Pawlas, V. Beneš, R. Hess, V. Schmidt (2017): On the computat

              probabilities based on a spatial stochastic model for precipitation cells and precipitat
              [ URL "https://link.springer.com/article/10.1007%2Fs00477-016-1321-8"] , Stoch. Env. Res
              31, 2659-2674.

            • D. Shalymov, O. Granichin, L. Klebanov, Z. Volkovich (2016): Literary writing style reco
              a minimum spanning tree-based approach [ URL "https://www.sciencedirect.com/science/arti
              S0957417416302573?via%3Dihub"] , Expert Syst. Appl., 61, 145-153.

            • J.H.G. Fu, D. Pokorný, J. Rataj (2017): Kinematic formulas for sets defined by differenc
              functions [ URL "https://www.sciencedirect.com/science/article/pii/S0001870816307903?via
              Math. 311, 796-832.

            • M. Neumann, C. Hirsch, J. Staněk, V. Beneš, V. Schmidt (2019): Estimation of geodesic to
              constrictivity in stationary random closed sets [ URL "https://onlinelibrary.wiley.com/d
              sjos.12375"] , Scand. J. Statist. 46, doi.org/10.1111/sjos.12375, in print.