## FG Mathematische Stochastik / Stochastische Prozesse in den Neurowissenschaften

4 Items

**Diffusivity estimation for activator–inhibitor models: Theory and application to intracellular dynamics of the actin cytoskeleton**

*Pasemann, Gregor ; Flemming, Sven ; Alonso, Sergio ; Beta, Carsten ; Stannat, Wilhelm* (2021-05-03)

A theory for diffusivity estimation for spatially extended activator–inhibitor dynamics modeling the evolution of intracellular signaling networks is developed in the mathematical framework of stochastic reaction–diffusion systems. In order to account for model uncertainties, we extend the results for parameter estimation for semilinear stochastic partial differential equations, as developed in...

**An Itô Formula for rough partial differential equations and some applications**

*Hocquet, Antoine ; Nilssen, Torstein* (2020-04-20)

We investigate existence, uniqueness and regularity for solutions of rough parabolic equations of the form ∂ t u − A t u − f = ( X ̇ t ( x ) ⋅ ∇ + Y ̇ t ( x ) ) u on [ 0 , T ] × ℝ d . To do so, we introduce a concept of “differential rough driver”, which comes with a counterpart of the usual controlled paths spaces in rough paths theory, built on the Sobolev spaces W k , p . We also define a na...

**Mathematical analysis of large-scale biological neural networks with delay**

*Mehri, Sima* (2019)

It is well-known that the components of the solution to a system of N interacting stochastic differential equations with an averaged sum of interaction terms and with independent identically distributed (chaotic) initial values, as N tends to infinity, converge to the solutions of Vlasov-McKean equations, in which the averaged sum is replaced by the expectation. Since the solutions to the corre...

**Finite-Size Effects on Traveling Wave Solutions to Neural Field Equations**

*Lang, Eva ; Stannat, Wilhelm* (2017-07-06)

Neural field equations are used to describe the spatio-temporal evolution of the activity in a network of synaptically coupled populations of neurons in the continuum limit. Their heuristic derivation involves two approximation steps. Under the assumption that each population in the network is large, the activity is described in terms of a population average. The discrete network is then approx...