2024/02/13 by Flandoli, Franco, Papini, Andrea, Marco Rehmeier +1 · 3 citations
Economics, Econometrics and Finance · #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2402.08461
We show that, in one spatial and arbitrary jump dimension, the averaged solution of a Marcustype SPDE with pure jump Lévy transport noise satisfies a dissipative deterministic equation involving a fractional Laplace-type operator. To this end, we identify the correct associated Lévy measure for the driving noise. We consider this a first step in the direction of a non-local version of enhanced dissipation, a phenomenon recently proven to occur for Brownian transport noise and the associated local parabolic PDE by the first author. Moreover, we present numerical simulations, supporting the fact that dissipation occurs for the averaged solution, with a behavior akin to the diffusion due to a fractional Laplacian, but not in a pathwise sense.The code produce 1-dimensional solutions for the proposed setting. The code is commented and incorperates the computation of the numerical solutions, the plots for the data and the non linear regression. Note that this is a working code, we'll modify the code in the future to polish it and add comments.