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学术报告


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  1 :    On the stochastic heat equation with sticky reflected boundary condition
:    Martin Grothaus
                  University of Kaiserslautern
    间:  2019910日(周二) 930—1030;
                  2019
911日(周三) 930—1030;
                  2019
912日(周四) 930—1030;
    点: 数学院南楼224
      :    Via Dirichlet form techniques we constructed a Markov process corresponding to the gradient Dirichlet form with respect to the law of the modulus of the Brownian bridge. The process is conjectured to be the scaling limit of the dynamical wetting model, also known as Ginzburg-Landau dynamics with pinning and reflection competing on the boundary. In order to identify the constructed process as a solution of the stochastic heat equation with boundary condition, we prove an integration by parts formula for modulus of the Brownian bridge. First we construct the generalized logarithmic derivative in the space of Hida distributions. In a second step we identify the obtained distribution with a regular countable additive set function in a Gelfand triple. This allows us to show that the constructed process is a solution to an infinite-dimensional Skorohod problem.
In a series of lectures I would like to explain in detail how an interplay between Dirichlet Forms, White Noise Analysis and Measure Theory in a Gelfand Triple enables us to solve this infinite dimensional Skorohod problem.

   2:    Stochastic PDEs with nonlocal operators driven by Lévy processes
:    Istvan Gyongy
                  University of Edinburgh
   间:    2019910日(周二) 1430—1530;
                   2019
911日(周三) 1430—1530;
                   2019
912日(周四) 1045—1145;   1430—1530.
   点:    数学院南楼224
     :    Second order stochastic parabolic integro-differential equations driven by Wiener processes and Poisson martingale measures are considered. They arise in nonlinear filtering of partially observable jump-diffusions, and in many areas of physics and engineering. These equations may degenerate and can be PDEs with lower order (possibly fractional) differential operators.
The main result presented in the lectures is an existence, uniqueness and regularity theorem for the solutions of these equations. Its proof will use interpolation theorems from harmonic analysis and an It? formula obtained recently in a joint paper with Sizhou Wu for It?-Lévy type processes.
If time permits some numerical methods to approximate the solutions will also be discussed.
he main part of the lectures is based on joint papers with Marta de León-Contreras and Sizhou Wu.

    3:    Monotonicity methods for SPDE, including the time fractional case
:    Michael Roeckner
                   Bielefeld University and AMSS
    间:   2019910日(周二) 1045—1145; 1545—1645;
                  2019
911日(周三) 1045—1145; 1545—1645;
                  2019
912日(周四) 1545—1645;
    点:    数学院南楼224
     :    In the first part of the lectures we shall give a concise overview on the theory and applications of SPDE with locally monotone coefficients under generalized growth and coercivity conditions. Applications include in particular classical cases as the stochastic 2D and 3D-Navier Stokes equations or the stochastic Cahn-Hilliard equation or surface growth models. The second part will be devoted to the time fractional case. A general well-posedness result including the underlying main ideas and sketch of the proof will be presented. Applications here include the stochastic porous media, fast diffusion and p-Laplace equations with fractional time derivative. Time permitting, a survey on various partly quite recent notions of solutions, as e.g. in the sense of stochastic variational inequalities or so-called variational solutions, which are minimizers of appropriate convex functionals on spaces of random paths, will be given.

    4:    Analysis on metric measure spaces and synthetic Ricci bounds
:    Karl-Theodor Sturm
                   University of Bonn
   间:    2019919日(周四) 1430—1530; 1545—1645;
                   2019
920日(周五) 1045—1145;
                   2019
920日(周五) 1430—1530; 1545—1645.
   点:    数学院南楼224
     :    The five lectures include:
(1)    Introduction to synthetic Ricci bounds;
(2)    Variable Ricci bounds: equivalence of Eulerian and Lagrangian approach to curvature-dimension conditions with variable curvature bounds;
(3)    Distributional valued Ricci bounds;
(4)    Time change, localization, and convexification;
(5)    Gradient estimates for Neumann heat flow on non-convex and convex domains.

    5:    McKean - Vlasov SDEs
:    Alexandre Veretennikov
                   University of Leeds
    间:  2019916日(周一) 930—1030; 1430—1530;
                  2019
917日(周二) 930—1030; 1430—1530;
   点:    数学院南楼224
   :      In the mini-course we will talk about some results on weak solutions, existence; weak uniqueness; strong existence and uniqueness of Mckean-Vlasov SDEs.

    6:    Stochastic Analysis on the space of measures
:    Feng-Yu Wang
                  Tianjin University
     间:  2019918日(周三) 1430—1530;
                   2019
919日(周四) 0930—1030;  1045—1145;
                   2019
920日(周五) 0930—1030;
                   2019
921日(周六) 0930—1030.
    点:    数学院南楼224
     :      The mini course consists of three parts. 
    In the first part we introduce some recent progress on functional inequalities for measure-valued diffusion processes associated with Dirichlet forms induced by the intrinsic and extrinsic derivatives and several different references probability measures.
   In the second part, we construct diffusion process on the Wasserstein space generated seance-order differential operators in the intrinsic derivative, and investigate the ergodicity and applications to PDEs on the Wasserstein space.
   In the last part, we introduce Harnack inequalities and the intrinsic derivative formulas for distribution-dependent (or McKean-Vlasov) SDEs.

    7:    Time-fractional stochastic conservation laws
:    Petra Wittbold
                   University of Duisburg-Essen
    间:   2019916日(周一) 1045—1145;  1545—1645;
                   2019
917日(周二) 1045—1145;  1545—1645;
                   2019
918日(周三) 1045—1145
    点:    数学院南楼224

      :  

  First lecture: fractional derivatives, examples and applications;

  Second lecture: fractional PDEs and their stochastic perturbation;
  Third lecture: conservation laws and entropy solutions (deterministic case);
  Fourth and fifth lecture: the analysis of the fractional stochastic conservation law.

    8:    Krylov's estimates and their applications in SDEs
:    Xicheng Zhang
                   Wuhan University
     间:  2019921日(周六) 1045—1145;
                   2019
921日(周六) 1430—1530;  1545—1645;
                   2019
922日(周日) 0930—1030;  1045—1145.
     点: 数学院南楼224

    :      In this talk I will introduce the classical Krylov estimate and its variant form. As applications, I will also introduce some applications in singular SDEs.

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