Large Deviations for a Stochastic Landau-Lifshitz-Gilbert Equation Driven by Pure Jump Noise
|Starts:||15:00 12 Feb 2020|
|Ends:||15:30 12 Feb 2020|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
We consider a one-dimensional stochastic Landau-Lifshitz-Gilbert equation with jump noise in the Marcus canonical form. We first show that there exists a strong solution to this equation, which is pathwise unique. We further show that this solution enjoys maximal regularity property. Next, we establish a Wentzell-Freidlin type large deviations principle for the small noise asymptotic of solutions using the weak convergence method.
We use the approach to the LDP based on the weak converegnce as in 6. We prove an appropriate version of the Girsanov Theorem based on 5.
The Marcus canonical form was introduced in 8 and mathematically developed by Applebaum and Kunita, see e.g. 7. Physical motivations can be found in e.g. 9.
This work generalises the case stochastic Landau-Lifshitz-Gilbert equation perturbed by a gaussian noise studied in 1 and 2.
This talk is based on a joint work 4 with Utpal Manna (Trivandrum) and Jianliang Zhai (Hefei).
Organisation: University of York
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Frank Adams 2
Alan Turing Building