7,402 research outputs found
Some numerical methods for solving stochastic impulse control in natural gas storage facilities
The valuation of gas storage facilities is characterized as a stochastic impulse control problem with finite horizon resulting in Hamilton-Jacobi-Bellman (HJB) equations for the value function. In this context the two catagories of solving schemes for optimal switching are discussed in a stochastic control framework. We reviewed some numerical methods which include approaches related to partial differential equations (PDEs), Markov chain approximation, nonparametric regression, quantization method and some practitioners’ methods. This paper considers optimal switching problem arising in valuation of gas storage contracts for leasing the storage facilities, and investigates the recent developments as well as their advantages and disadvantages of each scheme based on dynamic programming principle (DPP
Charge Quantization and Neutrino Mass from Planck-scale SUSY
We show a possibility for the charge quantization of the standard model (SM)
particles. If a global symmetry makes the three copies of a generation and
supersymmetry (SUSY) relates the Higgs boson to a lepton, all the charges of
the SM particles can be quantized through gauge-anomaly cancellation. In the
minimal model realizing the possibility, the gravitino mass around the
Planck-scale is needed to generate the SM couplings through (quantum)
supergravity. Much below the Planck-scale, the SM is obtained as the effective
theory. Interestingly, if the gaugino masses are generated through anomaly
mediation, one of the neutrino masses is predicted to be around the neutrino
oscillation scales. In an extension of the model, millicharged particles can
exist without introducing massless hidden photons.Comment: 17 pages, v2: version appears in PL
Two-scale large deviations for chemical reaction kinetics through second quantization path integral
Motivated by the study of rare events for a typical genetic switching model
in systems biology, in this paper we aim to establish the general two-scale
large deviations for chemical reaction systems. We build a formal approach to
explicitly obtain the large deviation rate functionals for the considered
two-scale processes based upon the second-quantization path integral technique.
We get three important types of large deviation results when the underlying two
times scales are in three different regimes. This is realized by singular
perturbation analysis to the rate functionals obtained by path integral. We
find that the three regimes possess the same deterministic mean-field limit but
completely different chemical Langevin approximations. The obtained results are
natural extensions of the classical large volume limit for chemical reactions.
We also discuss its implication on the single-molecule Michaelis-Menten
kinetics. Our framework and results can be applied to understand general
multi-scale systems including diffusion processes
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