Infinitesimal generator
Encyclopedia
In mathematics
, the term infinitesimal generator may refer to:
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the term infinitesimal generator may refer to:
- an element of the Lie algebraLie algebraIn mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" was introduced by Hermann Weyl in the...
associated to a Lie groupLie groupIn mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
; - the infinitesimal generatorInfinitesimal generator (stochastic processes)In mathematics — specifically, in stochastic analysis — the infinitesimal generator of a stochastic process is a partial differential operator that encodes a great deal of information about the process...
of a stochastic process; - the infinitesimal generator of a strongly continuous semigroup.