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Results tagged with stochastic-processes
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user 29661
A stochastic process is a collection of random variables usually indexed by a totally ordered set.
1
vote
1
answer
244
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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(-{ …
- 135
1
vote
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
6
votes
2
answers
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Ito diffusion with highly oscillatory diffusion coefficient
Consider the stochastic differential equation on $\mathbb R$
$$
dx_t = f(x_t) dt + g(\omega t)\, dW_t
$$
with $W_t$ a standard Brownian motion, $f:\mathbb R \to \mathbb R$ a smooth function, and $g: …
- 135