• 10:50 - 11:35 M. Röckner (Bielefeld Universität): The Stochastic Porous Media Equations on d
  • This talk is on existence and uniqueness of solutions to the stochastic porous media equation dX - Δψ(X)dt = XdW on d. Here, W is a Wiener process and ψ is a maximal monotone graph in ℝxℝ such that ψ(r)≤ C(|r|m + 1), for every r∈ℝ. In this general case the dimension is restricted to d>3. When ψ is Lipschitz, the well-posedness, however, holds for all dimensions on the classical Sobolev space H-1(ℝd). If ψ(r)r≥ρ|r|m+1 and m:= (d-2)/(d+2), we prove finite time extinction of the solutions with strictly positive probability.
  • 11:45 - 12:30 M. Neklyudov (Università di Pisa): New type of homogenisation problem for stochastic parabolic equations
  • We will show that the solution of 1D stochastic parabolic equation with additive noise converges to a diffusion process independent upon space variable when we rescale noise at the extremum points of the process. We will discuss open problems and suggest future directions of research. The talk is based on a joint work in progress with Ben Goldys.
  • 12:30 - 14:20 Lunch break
  • 14:20 - 15:05 C. Olivera (Universidade Estadual de Campinas): On a class of stochastic transport equations for L2loc vector fields
  • We study in this talk the existence and uniqueness of solutions to a class of stochastic transport equations with irregular coefficients. Asking only boundedness of the divergence of the coefficients (a classical condition in both the deterministic and stochastic setting), we can lower the integrability regularity required in known results on the coefficients themselves and on the initial condition, and still prove uniqueness of solutions.
  • 15:15 - 16:00 M. Leimbach (TU Berlin): Blow-up of stable stochastic differential equation
  • We examine a 2-dimensional ODE which exhibits explosion in finite time. Considered as an SDE with additive white noise, it is known to be complete - in the sense that for each initial condition there is almost surely no explosion. Furthermore, the associated Markov process even admits an invariant probability measure. On the other hand, as we will show, the corresponding local stochastic flow will almost surely not be strongly complete, i.e. there exist (random) initial conditions for which the solutions explode in finite time.

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Aula Magna

Dipartimento di Matematica

Università di Pisa

Largo Bruno Pontecorvo 5

56127 Pisa



Supported by the project PRIN 2011: Equazioni differenziali stocastiche