2026· International Journal of Mathematical Analysis· 0 citations· 13 references
Abstract
This paper develops a time-inhomogeneous Ito diffusion population model subject to multiplicative random catastrophes. Closed-form transient moments of arbitrary integer order are derived. For a homogeneous benchmark, the expected-population exponent depends on E[Y], whereas the almost-sure sample-path exponent depends on E[log Y] and the diffusion correction. This creates a parameter region in which the expected population grows while typical sample paths decline exponentially. A nonnegative mean-path gap is obtained from log y <= y-1. Random catastrophe severity and seasonal environments are also considered. Monte Carlo experiments illustrate that a rising ensemble mean can coexist with a sharply declining median population.
This paper develops a random-effects extension of the ergodic basic affine jump-diffusion (BAJD) model for a population of independent trajectories with individual unobserved jump intensities and common structural parameters. Under continuous-time observation, each intensity is estimated by the empirical jump frequency...
A Hawkes process is a simple point process whose intensity depends on its history; the resulting dynamics are generally non-Markovian. We establish a sample-path moderate deviation principle for a nonlinear Hawkes process in the full moderate regime. Since a Poisson cluster representation is unavailable for nonlinear H...
This paper introduces a set of bounded continuous-time diffusion models with standard and modified Kumaraswamy distributions as their invariant and limiting distributions. Both Kumaraswamy distributions, including their reflected versions, are considered. The models are constructed through transformations of Jacobi dif...
Karl Larsson· Stochastic environmental res...· 0 citations
This paper develops a stochastic susceptible–infected–hesitating–removed (SIHR) rumor model with Hill-type saturated incidence and compartment-specific Brownian perturbations. The model focuses on when environmental noise changes a rumor’s deterministic fate and how long-run behavior is organized as an invariant law ra...
We develop and analyze a Monte Carlo method for sampling killed anomalous diffusions obtained by time-changing Brownian motion with drift by the inverse of a subordinator. The method targets probabilistic representations of time-nonlocal, including time-fractional, Cauchy--Dirichlet problems on bounded domains. Since i...
I. Biočić, Daniel E. Cedeño-Girón, Aleksandar Mijatovic et al.· 0 citations
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