Wellposedness and large deviations of fractional McKeanVlasov stochastic reactiondiffusion equations on unbounded domains
Abstract
This paper is mainly concerned with the large deviation principle of the fractional McKeanVlasov stochastic reactiondiffusion equation defined on R^n with polynomial drift of any degree. We first prove the wellposedness of the underlying equation under a dissipative condition, and then show the strong convergence of solutions of the corresponding controlled equation with respect to the weak topology of controls, by employing the idea of uniform tailends estimates of solutions in order to circumvent the noncompactness of Sobolev embeddings on unbounded domains. We finally establish the large deviation principle of the fractional McKeanVlasov equation by the weak convergence method without assuming the time Holder continuity of the nonautonomous diffusion coefficients.
 Publication:

arXiv eprints
 Pub Date:
 June 2024
 DOI:
 10.48550/arXiv.2406.10694
 arXiv:
 arXiv:2406.10694
 Bibcode:
 2024arXiv240610694C
 Keywords:

 Mathematics  Probability;
 Mathematics  Analysis of PDEs;
 60F10;
 60H15;
 37L55;
 35R60