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 also be identified as a stochastic Lotka-Volterra type population model. Infinite behavior such as explosion/nonexplosion for this population and staying infinite/coming down from infinity are derived under various conditions on the coefficients involved in the model and the conclusions are rather sharp
We develop a stochastic diffusion model with two component Allee effects via a continu- um limit of a discrete Markov process. The boundary classification proves that zero is exit and infinity is entrance. Using intrinsic ultracontractivity of the associated semigroup, we establish the existence and uniqueness of a qua...
Gui-Jie Lan· International Journal of Bio...· 0 citations
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 we...
N. Ratanov· Markov Processes and Related...· 0 citations
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...
Qing-Yan Meng, Jin-Qiao Duan, V. Lucarini· 0 citations
We develop a spectral theory for dynamical large deviations in non-Markov jump processes and non-Markov chains, whose dynamics depends on the past through state- and jump-dependent empirical observables. We demonstrate that a multiscale Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) Ansatz separates fast configurational rel...
We obtain a complete characterization of the quasi-stationary distributions of subcritical stable continuous-state branching processes in Brownian random environments, together with the domain of attraction of each member. These distributions form a one-parameter family whose modified Laplace transforms are given expli...
Pei-Sen Li· 0 citations
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