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View article: Exponential contraction in impulsive stochastic differential equations: Analysis of exact and numerical solutions
Exponential contraction in impulsive stochastic differential equations: Analysis of exact and numerical solutions Open
In this paper, we examine the moment exponential contraction in stochastic differential equations with impulsive perturbations, with a focus on the small-moments of distances between solutions. A criterion for this contraction is establish…
View article: A class of long-run average control problems of Lotka-Voltera systems in a stochastic environment
A class of long-run average control problems of Lotka-Voltera systems in a stochastic environment Open
This work is devoted to studying a class of biological control problems in a stochastic environment. Specifically, it focuses on stochastic Lotka-Voltera systems. Our effort is on treating average cost per unit time controlled diffusions. …
View article: Chemoproteomics identifies proteoform-selective caspase-2 inhibitors
Chemoproteomics identifies proteoform-selective caspase-2 inhibitors Open
Caspases are a highly conserved family of cysteine-aspartyl proteases known for their essential roles in regulating apoptosis, inflammation, cell differentiation, and proliferation. Complementary to genetic approaches, small-molecule probe…
View article: Stability in distribution and stabilization of switching jump diffusions
Stability in distribution and stabilization of switching jump diffusions Open
This paper aims to study stability in distribution of Markovian switching jump diffusions. The main motivation stems from stability and stabilizing hybrid systems in which there is no trivial solution. An explicit criterion for stability i…
View article: A survey of numerical solutions for stochastic control problems: Some recent progress
A survey of numerical solutions for stochastic control problems: Some recent progress Open
This paper presents a survey on some of the recent progress on numerical solutions for controlled switching diffusions. We begin by recalling the basics of switching diffusions and controlled switching diffusions. We then present regular c…
View article: Harvesting of a stochastic population under a mixed regular-singular control formulation
Harvesting of a stochastic population under a mixed regular-singular control formulation Open
This work focuses on optimal harvesting-renewing for a stochastic population. A mixed regular-singular control formulation with a state constraint and regime-switching is introduced. The decision-makers either harvest or renew with finite …
View article: The effects of random and seasonal environmental fluctuations on optimal harvesting and stocking
The effects of random and seasonal environmental fluctuations on optimal harvesting and stocking Open
We analyze the harvesting and stocking of a population that is affected by random and seasonal environmental fluctuations. The main novelty comes from having three layers of environmental fluctuations. The first layer is due to the environ…
View article: Marine Network Protocols and Security Risks
Marine Network Protocols and Security Risks Open
Marine network protocols are domain-specific network protocols that aim to incorporate particular features within the specialized marine context that devices are implemented in. Devices implemented in such vessels involve critical equipmen…
View article: Optimal Control and Numerical Methods for Hybrid Stochastic SIS Models
Optimal Control and Numerical Methods for Hybrid Stochastic SIS Models Open
This work focuses on optimal controls of a class of stochastic SIS epidemic models under regime switching. By assuming that a decision maker can either influence the infectivity period or isolate infected individuals, our aim is to minimiz…
View article: Properties of switching jump diffusions: Maximum principles and Harnack inequalities
Properties of switching jump diffusions: Maximum principles and Harnack inequalities Open
This work examines a class of switching jump diffusion processes. The main effort is devoted to proving the maximum principle and obtaining the Harnack inequalities. Compared with the diffusions and switching diffusions, the associated ope…
View article: Extinction and permanence in a stochastic SIRS model in regime-switching with general incidence rate
Extinction and permanence in a stochastic SIRS model in regime-switching with general incidence rate Open
In this paper, we consider a stochastic SIRS model with general incidence rate and perturbed by both white noise and color noise. We determine the threshold $λ$ that is used to classify the extinction and permanence of the disease. In part…
View article: Harvesting of interacting stochastic populations
Harvesting of interacting stochastic populations Open
We analyze the optimal harvesting problem for an ecosystem of species that experience environmental stochasticity. Our work generalizes the current literature significantly by taking into account non-linear interactions between species, st…
View article: Properties of Switching Jump Diffusions: Maximum Principles and Harnack Inequalities
Properties of Switching Jump Diffusions: Maximum Principles and Harnack Inequalities Open
This work examines a class of switching jump diffusion processes. The main effort is devoted to proving the maximum principle and obtaining the Harnack inequalities. Compared with the diffusions and switching diffusions, the associated ope…
View article: Recurrence and Ergodicity for A Class of Regime-Switching Jump Diffusions
Recurrence and Ergodicity for A Class of Regime-Switching Jump Diffusions Open
This work develops asymptotic properties of a class of switching jump diffusion processes. The processes under consideration may be viewed as a number of jump diffusion processes modulated by a random switching mechanism. The underlying pr…
View article: Optimal harvesting strategies for stochastic ecosystems
Optimal harvesting strategies for stochastic ecosystems Open
Focusing on multidimensional stochastic Lotka–Volterra type ecosystems in which multiple species are interacting, this study aims developing optimal harvesting strategies. The underlying systems are controlled regime‐switching diffusions. …
View article: Nonlinear Stochastic Systems And Controls: Lotka-Volterra Type Models, Permanence And Extinction, Optimal Harvesting Strategies, And Numerical Methods For Systems Under Partial Observations
Nonlinear Stochastic Systems And Controls: Lotka-Volterra Type Models, Permanence And Extinction, Optimal Harvesting Strategies, And Numerical Methods For Systems Under Partial Observations Open
This dissertation focuses on a class of stochastic models formulated using stochastic differential equations with regime switching represented by a continuous-time Markov chain, which also known as hybrid switching diffusion processes. Our…