In this paper, we study a piecewise-deterministic stochastic process governed by a double-well potential. The dynamics are randomised through resets to a random point, occurring after independent and exponentially distributed time intervals. Distributions of the particle’s position are presented for a fixed time, as well as in the limit as t → ∞.
We consider discrete-time non-linear stochastic dynamical systems where the driving noise is not i.i.d. but an autoregressive process (``red noise''). Under a standard dissipativity condition, we prove geometrically fast convergence to a stationary distribution in total variation.
In this paper we consider a two-dimensional generalized continuous-state branching process with mutually enhancing two-way interactions characterized by two stochastic differential equations driven by Brownian motions and spectrally positive $\alpha$-stable random measures. Such continuous-state population dynamics can...
In this paper we study the constant speed, biased random walk in dynamical random conductances. In certain regimes of the parameters of the model, we prove that the random walk is ballistic. We show annealed and quenched CLT in the full parameter range. Furthermore, as a consequence of the non-reversible nature of this...
In this paper, we will propose a new noise and establish a stochastic calculus driven by this noise in which we find its characteristics, the stochastic integration, Itô's formula and stochastic differential equation.
In this paper, we develop a linear response theory for a class of stochastic differential equations driven by jump processes. We investigate the response of the system to small time-dependent perturbations from three complementary perspectives: probability density functions, mean exit times, and escape probabilities. B...
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