Large-time behavior of non-symmetric Fokker-Planck type equations | Zendy

Anton Arnold | Zendy; Eric A. Carlen | Zendy; Qiangchang Ju | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Large-time behavior of non-symmetric Fokker-Planck type equations

Author(s) -

Anton Arnold,

Eric A. Carlen,

Qiangchang Ju

Publication year - 2008

Publication title -

communications on stochastic analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.224

H-Index - 10

eISSN - 2688-6669

pISSN - 0973-9599

DOI - 10.31390/cosa.2.1.11

Subject(s) - fokker–planck equation , logarithm , mathematics , skew , type (biology) , constant (computer programming) , entropy (arrow of time) , operator (biology) , steady state (chemistry) , mathematical analysis , sobolev inequality , planck , sobolev space , statistical physics , physics , quantum mechanics , differential equation , computer science , ecology , biochemistry , chemistry , repressor , astronomy , transcription factor , gene , biology , programming language

Large time asymptotics of the solutions to non-symmetric Fokker- Planck type equations are studied by extending the entropy method to this case. We present a modified Bakry-Emery criterion that yields covergence of the solution to the steady state in relative entropy with an explicit exponen- tial rate. In parallel it also implies a logarithmic Sobolev inequality w.r.t. the steady state measure. Explicit examples illustrate that skew-symmetric per- turbations in the Fokker Planck operator can "help" to improve the constant in such a logarithmic Sobolev inequality.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research