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The Wiener Measure on the Heisenberg Group and Parabolic Equations
- Source :
- Journal of Mathematical Sciences. 245:155-177
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- In this paper, we study questions related to the theory of stochastic processes on Lie nilpotent groups. In particular, we consider the stochastic process on the Heisenberg group H3(ℝ) whose trajectories satisfy the horizontal conditions in the stochastic sense relative to the standard contact structure on H3 (ℝ). It is shown that this process is a homogeneous Markov process relative to the Heisenberg group operation. There was found a representation in the form of a Wiener integral for a one-parameter linear semigroup of operators for which the Heisenberg sublaplacian generated by basis vector fields of the corresponding Lie algebra L(H3) is producing. The main method of solving the problem in this paper is using the path integrals technique, which indicates the common direction of further development of the results.
- Subjects :
- Statistics and Probability
Pure mathematics
Semigroup
Stochastic process
Applied Mathematics
General Mathematics
010102 general mathematics
Markov process
01 natural sciences
Measure (mathematics)
010305 fluids & plasmas
Nilpotent
symbols.namesake
0103 physical sciences
Path integral formulation
Lie algebra
symbols
Heisenberg group
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 15738795 and 10723374
- Volume :
- 245
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematical Sciences
- Accession number :
- edsair.doi...........8cbb6716ae2d6b9045da71f44000ae1c