Jiyeon Lee

A model for a system subject to random shocks

A Markovian stochastic model for a system subject to random shocks is introduced. It is assumed that the shock arriving according to a Poisson process decreases the state of the system by a random amount. It is further assumed that the system is repaired by a repairman arriving according to another Poisson process if the state when he arrives is below a threshold a. Explicit expressions are deduced for the characteristic function of the distribution function of X(t), the state of the system at time t, and for the distribution function of X(t), if X(t) I> a. The stationary case is also discussed.

First exit times for compound Poisson dams with a general release rule

An infinite dam with compound Poisson inputs and a state-dependent release rate is considered. For this dam, we solve Kolmogorov’s backward differential equation to obtain the Laplace transforms of the first exit times in terms of a certain positive kernel. This allows us to provide an explicit expression for the Laplace transform of the wet period for a finite dam.

Dielectric, Thermally Stimulated Discharge Current, Pyroelectric and Surface Morphology of Pmma Thin Films Prepared by Isothermal Immersion

Metal–Insulator–Metal structure was used to investigate the dielectric, thermally stimulated discharge current(TSDC)and pyroelectric behavior of poly methyl methacrylate(PMMA)thin films prepared by isothermal immersion method. The surface morphology and the structure of the above said films were studied by using atomic force microscopy(AFM)and X-ray diffraction(XRD)respectively. The XRD spectrum of as grown and films annealed at 513 K indicated the amorphous nature. No pits and dendritic features were observed from the AFM spectrum. The only important topographic features observed is the hillocks of about 10–12 nm large with a peak to valley vertical distance of about 0.5–1 nm. Both as grown and films annealed at 513 K showed very smooth surface and amorphous nature. From the TSDC spectrum activation energy(E), capture cross-section(σ), escape frequency(ν)and relaxation time(τ)were calculated. The observed amorphous phase, low loss, dielectric and thermal behavior imply the feasibility of utilizing PMMA thin films as gate dielectric insulator layer in organic thin film transistors(OTFTs), which can find application in flat panel display.

A discrete dynamical system for the greedy strategy at collective Parrondo games

We consider a collective version of Parrondos games with probabilities parameterized by ρ ∈ (0, 1) in which a fraction φ ∈ (0, 1] of an infinite number of players collectively choose and individually play at each turn the game that yields the maximum average profit at that turn. Dinís and Parrondo [L. Dinís and J.M.R. Parrondo, Optimal strategies in collective Parrondo games, Europhys. Lett. 63 (2003), pp. 319–325] and Van den Broeck and Cleuren [C. Van den Broeck and B. Cleuren, Parrondo games with strategy, in Noise in Complex Systems and Stochastic Dynamics II, Z. Gingl, J.M. Sancho, L. Schimansky-Geier, and J. Kertesz, eds., SPIE, Bellingham, WA, 2004, pp. 109–118.] studied the asymptotic behaviour of this greedy strategy, which corresponds to a piecewise-linear discrete dynamical system in a subset of the plane, for ρ = 1/3 and three choices of φ. We study its asymptotic behaviour for all (ρ, φ) ∈ (0, 1) × (0, 1], finding that there is a globally asymptotically stable equilibrium if φ ≤ 2/3 and, typically, a unique (asymptotically stable) limit cycle if φ > 2/3 (‘typically’ because there are rare cases with two limit cycles). Asymptotic stability results for φ > 2/3 are partly conjectural.

Asymptotics of overflow probabilities in Jackson networks

We consider the probability that the total population of a Jackson network exceeds a given large value. By using the relation to the stationary distribution, we derive upper and lower bounds on this probability. These bounds imply a stronger logarithmic limit when multiple nodes have the same maximal load.

Optimal control of a model for a system subject to random shocks

A Markovian stochastic model for a system subject to random shocks is considered. Each shock arriving according to a Poisson process decreases the state of the system by a random amount. A repairman arriving according to another Poisson process repairs the system only if the state is below a threshold. Costs are assigned to each visit of the repairman, to each repair, and to the system being in bad states below the threshold. It is shown that there exists a unique arrival rate of the repairman which minimizes the expected long-run average cost.

An optimal proportion of perfect repair

At each failure of a system, with probability p it is perfectly repaired, and with probability 1-p it is restored to its condition just prior to failure. It is shown that there exists a unique p minimizing the long-run repair cost, provided the failure time distribution of the system has strictly DMRL.

Ruin Probability in a Compound Poisson Risk Model with a Two-Step Premium Rule

We consider a compound Poisson risk model in which the premiums may depend on the state of the surplus process. By using the overflow probability of the workload process in the corresponding M/G/1 queueing model, we obtain the probability that the ruin occurs before the surplus reaches a given large value in the risk model. We also examplify the ruin probability in case of exponential claims.

The flashing Brownian ratchet and Parrondo’s paradox

A Brownian ratchet is a one-dimensional diffusion process that drifts towards a minimum of a periodic asymmetric sawtooth potential. A flashing Brownian ratchet is a process that alternates between two regimes, a one-dimensional Brownian motion and a Brownian ratchet, producing directed motion. These processes have been of interest to physicists and biologists for nearly 25 years. The flashing Brownian ratchet is the process that motivated Parrondo’s paradox, in which two fair games of chance, when alternated, produce a winning game. Parrondo’s games are relatively simple, being discrete in time and space. The flashing Brownian ratchet is rather more complicated. We show how one can study the latter process numerically using a random walk approximation.

A Compound Poisson Risk Model with a Two-Step Premium Rule

We consider a compound Poisson risk model in which the premium rate changes when the surplus exceeds a threshold. The explicit form of the ruin probability for the risk model is obtained by deriving and using the overflow probability of the workload process in the corresponding M/G/1 queueing model.