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Results tagged with ds.dynamical-systems
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user 29661
Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.
1
vote
1
answer
244
views
Langevin equation with position-dependant damping: existence of an invariant measure?
The usual Langevin equation for a particle in a 1D harmonic potential
$dq(t) = p(t)~dt$
$dp(t) = -q(t)~dt + a ~dW(t) - b~p(t)~dt$
admits as an invariant measure the Gibbs measure ${1\over Z}\exp(-{ …
- 365
1
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0
answers
163
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Adding a damping term to a dynamical system or Markov process: what happens to invariant mea...
Consider the continuous-time Markov process on ${\mathbb R}^n$ described by the SDE
$\dot{x}(t) = F(x(t)) + \xi(t)$
where $F:{\mathbb R}^n \to {\mathbb R}^n$ is a smooth mapping, and $\xi(t)$ is a w …
- 135