Monday, October 14, 2019 - 13:00 in V3-201
A short overview of my PhD-project: Stochastic Transport Equations: Method of Characteristics versus Scaling Transform Approach
A talk in the Cluster Group Stochastic Analysis series by
Nora Müller from Bielefeld
| Abstract: |
In this talk I will give a short overview of my PhD-thesis. We consider general stochastic transport equations in dimension 1 of the form
\begin{align*}
\mathrm{d} u (x,t) = {\phi(x,t)} &\frac{\partial u}{\partial x}(x,t) \,\mathrm{d} t - {\psi(x,t) u(x,t)} \,\mathrm{d} t
\\&- {\lambda u(x,t)|u(x,t)|^{q-2}}\,\mathrm{d} t + {u(x,t)\,\mathrm{d} \mathbb{W}(x,t)}
\end{align*}
where $\mathbb{W}(x,t)$ denotes a general Wiener process. After a brief repetition of the well-known method of characteristics, we introduce a heuristic approach of its stochastic version, the so called method of stochastic characteristics and apply it to the equation.
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