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Lina Ji

Publications and source records attributed to Lina Ji.

11 recordsLinked to original sources
arXiv2026

Extinction and extinguishment properties for a nonlinear predator-prey branching model

We study extinction and extinguishment in a two-type continuous-state nonlinear branching model driven by Brownian branching noise and spectrally positive stable jumps. The populations are subject to nonlinear self-regulation and a mixed-sign predator--prey interaction: the second promotes the first, whereas the first suppresses the second. Two complementary structures are developed. An exact power--logarithmic cancellation functional removes the interaction drifts and yields stochastic Lyapunov estimates, nonexplosion, and boundary criteria. In the multiplicative regimes, integrating-factor identities and geometric L\'evy factorizations express extinction through weighted exposure clocks and reduce the long-time analysis to effective decay rates. These methods yield almost-sure extinction criteria and identify a regime in which finite-time extinction and nonextinction coexist. On nonextinction, both populations remain positive at all finite times and converge jointly to zero, exhibiting joint extinguishment rather than positive persistence.

math.PR↗
arXiv2026

Mean-field branching SDEs: propagation of chaos, scaling limits and phase transitions

We study branching SDEs with law-dependent immigration and their mean-field particle approximations. Under a dissipativity condition and sufficiently weak interaction, a uniform propagation-of-chaos bound in time of order $N^{-1/2}$ is established. On every fixed finite time horizon, the same order of propagation of chaos holds for arbitrary finite interaction strength. A two-stage scaling limit connects continuous-time discrete-state mean-field birth--death processes to interacting branching diffusions and then to the nonlinear equation. For a logistic mean-field diffusion we prove a sharp criterion for extinction/non-extinction, and further show that weak enough interaction strength is necessary for a uniform-in-time approximation.

math.PR↗
arXiv2025

Threshold Diffusions

We propose threshold diffusion processes as unique solutions to stochastic differential equations with step-function coefficients, and obtain explicit expressions for the conditional Laplace transform of the hitting times and the potential measures. Applying these results, we further discuss their asymptotic behaviors such as the stationary distributions and the escape probabilities.

math.PR↗
arXiv2025

Boundary behavior at infinity for simple exchangeable fragmentation-coagulation process in critical slow regime

For a critical simple exchangeable fragmentation-coagulation process in slow regime where the coagulation rate and fragmentation rate are of the same order, we show that there exist phase transitions for its boundary behavior at infinity depending on the asymptotics of the difference between the two rates, and find rather sharp conditions for different boundary behaviors.

math.PR↗
arXiv2024

Exponential Ergodicity of CBIRE-Processes with Competition and Catastrophes

We establish the exponential ergodic property in a weighted total variation distance of continuous-state branching processes with immigration in random environments with competition and catastrophes, under a Lyapunov-type condition and other mild assumptions. The proof is based on a Markov coupling process along with some delicate estimates for the associated coupling generator. In particular, the main result indicates whether and how the competition mechanism, the environment and the catastrophe could balance the branching mechanism respectively to guarantee the exponential ergodicity of the process.

math.PR↗
arXiv2023

Mixed state branching evolution for cell division models

We prove a scaling limit theorem for two-type Galton-Waston branching processes with interaction. The limit theorem gives rise to a class of mixed state branching processes with interaction using to simulate the evolution for cell division affected by parasites. Such process can also be obtained by the pathwise unique solution to a stochastic equation system. Moreover, we present sufficient conditions for extinction with probability one and the exponential ergodicity in the total variation distance of such process.

math.PR↗
arXiv2023

Well-posedness of the martingale problem for super-Brownian motion with interactive branching

In this paper a martingale problem for super-Brownian motion with interactive branching is derived. The uniqueness of the solution to the martingale problem is obtained by using the pathwise uniqueness of the solution to a corresponding system of SPDEs with proper boundary conditions. The existence of the solution to the martingale problem and the local Hölder continuity of the density process are also studied.

math.PR↗
arXiv2021

Well-posedness of martingale problem for SBM with interacting branching

In this paper a martingale problem for super-Brownian motion with interactive branching is derived. The uniqueness of the solution to the martingale problem is obtained by using the pathwise uniqueness of the solution to a corresponding system of SPDEs with proper boundary conditions. The existence of the solution to the martingale problem and the Holder continuity of the density process are also studied.

math.PR↗
arXiv2021

Mutually interacting superprocesses with migration

A system of mutually interacting superprocesses with migration is constructed as the limit of a sequence of branching particle systems arising from population models. The uniqueness in law of the superprocesses is established using the pathwise uniqueness of a system of stochastic partial differential equations with non-Lipschitz coefficients, which is satisfied by the corresponding system of distribution-function-valued processes.

math.PR↗
arXiv2017

Moments of continuous-state branching processes with or without immigration

For a positive continuous function f satisfying some standard conditions, we study the f-moments of continuous-state branching processes with or without immigration. The main results give criteria for the existence of the f-moments. The characterization of the processes in terms of stochastic equations given by Dawson and Li (2012) plays an essential role in the proofs.

math.PR↗