Infinite-dimensional Kolmogorov equations. (English) Zbl 1369.35111
Charpentier, Éric (ed.) et al., Kolmogorov’s heritage in mathematics. Transl. from the French. Berlin: Springer (ISBN 978-3-540-36349-1/hbk). 67-96 (2007).
Summary: In [Math. Ann. 104, 415–458 (1931; Zbl 0001.14902; JFM 57.0613.03)] A. N. Kolmogorov introduced very important partial differential equations. In the recent past years there was an increasing interest, due to applications in physics and in particular in statistical mechanics, to consider Kolmogorov equations in the extended context of infinite-dimensional Hilbert spaces. The aim of this chapter is to describe the “status of art” in this domain. We present different methods which have been used to solve these equations, as well as applications to some relevant stochastic partial differential equations.
For the entire collection see [Zbl 1136.00010].
For the entire collection see [Zbl 1136.00010].
MSC:
| 35R15 | PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) |
| 35Q82 | PDEs in connection with statistical mechanics |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60J25 | Continuous-time Markov processes on general state spaces |
| 47Dxx | Groups and semigroups of linear operators, their generalizations and applications |
