2
votes
1answer
292 views

Dynamics of Master Equation

I'm going to do research on dynamics of master equation of $n$ states $$\dot p_i=A_{ij}p_j\qquad i=1\ldots n$$ where $p_i$ is the $i$-th component of probability vector and $A_{ij}$ is transition rate ...
1
vote
0answers
103 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 ...
1
vote
0answers
108 views

Adding a damping term to a dynamical system or Markov process: what happens to invariant measures?

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 ...
5
votes
2answers
208 views

Liverani's CLT (a question)

Let $(\Omega,\mathcal{F},P)$ be a probability space where $\Omega$ is a complete separable metric space, let $T:\Omega\to \Omega$ ` be an ergodic transformation, let $\hat{T}:L^{2}_{_P}(\Omega)\to ...
2
votes
2answers
477 views

Midpoint lattice polygons

Midpoint polygons (a.k.a Kasner polygons) have been studied, and their behavior is well understood. I am considering a variant, which I call midpoint lattice polygons. Start with a sequence of ...