More Like this

1. Multi-dimensional Lévy Processes for Multiple Dependent Degradation Processes in Lifetime Analysis

   Shi, Y; Shu, Y; Feng, Q. (May 2018, Proceedings of Industrial and Systems Engineering Research Conference)

   The analysis of multiple dependent degradation processes is a challenging research work in the reliability field, especially for complex degradation with random jumps. To integrally handle the jump uncertainties in degradation and the dependence among degradation processes, we construct multi-dimensional Lévy processes to describe multiple dependent degradation processes in engineering systems. The evolution of each degradation process can be modeled by a one-dimensional Lévy subordinator with a marginal Lévy measure, and the dependence among all dimensions can be described by Lévy copulas and the associated multiple-dimensional Lévy measure. This Lévy measure is obtained from all its one-dimensional marginal Lévy measures and the Lévy copula. We develop the Fokker-Planck equations to describe the probability density in stochastic systems. The Laplace transforms of both reliability function and lifetime moments are derived. Numerical examples are used to demonstrate our models in lifetime analysis. 

   more » « less
2. Lévy Processes in a Step 3 Nilpotent Lie Group

   https://doi.org/10.1007/s11118-013-9373-6  

   Gordina, Maria; Haga, John (August 2014, Potential Analysis)
3. Optimal Periodic Replenishment Policies for Spectrally Positive Lévy Demand Processes

   Pérez, José-Luis; Yamazaki, Kazutoshi; Bensoussan, Alain (January 2020, SIAM journal on control and optimization)

   null (Ed.)

   We consider a version of the stochastic inventory control problem for a spectrally positive Lévy demand process, in which the inventory can only be replenished at independent exponential times. We show the optimality of a periodic barrier replenishment policy that restocks any shortage below a certain threshold at each replenishment opportunity. The optimal policies and value functions are concisely written in terms of the scale functions. Numerical results are also provided. 

   more » « less
4. Optimal Periodic Replenishment Policies for Spectrally Positive Lévy Demand Processes

   https://doi.org/10.1137/18M1196406  

   Pérez, José-Luis; Yamazaki, Kazutoshi; Bensoussan, Alain (January 2020, SIAM Journal on Control and Optimization)

   null (Ed.)
5. Diffusions on a space of interval partitions: construction from marked Lévy processes

   https://doi.org/10.1214/20-EJP521  

   Forman, Noah; Pal, Soumik; Rizzolo, Douglas; Winkel, Matthias (January 2020, Electronic Journal of Probability)

   null (Ed.)