We introduce a one-dimensional non-equilibrium lattice gas model representing the processive motion of dynein molecular motors over microtubule. study both dynamical and stationary state properties for consisting hardcore particles hopping on with variable step sizes. find that gap-distribution exhibits striking peaks around gap sizes are multiples maximum size, open periodic boundary condition...

Consider a periodic, mean-reverting Ornstein–Uhlenbeck process \(X=\{X_t,t\ge 0\}\) of the form \(d X_{t}=\left( L(t)+\alpha X_{t}\right) d t+ dB^H_{t}, \quad t \ge 0\), where \(L(t)=\sum _{i=1}^{p}\mu _i\phi _i (t)\) is periodic parametric function, and \(\{B^H_t,t\ge fractional Brownian motion Hurst parameter \(\frac{1}{2}\le H<1\). In “ergodic” case \(\alpha <0\), estimation \((\mu _1,\ldots...