Abstract
Stochastic processes of bounded variation are generated based on their two most important characteristics: spectral density functions and probability density functions. Two models are presented for the purpose: the randomized harmonic model and the nonlinear filter model. In the randomized harmonic model, a random noise is introduced in the phase angle; while in the nonlinear filter model, a set of nonlinear Ito differential equations are employed. In both methods, the spectral density of a stochastic process to be modeled, either with one peak or with multiple peaks, can be matched by adjusting model parameters. However, the probability density of the process generated by the randomized harmonic model has a fixed shape and cannot be adjusted. On the other hand, the nonlinear filter model covers a variety of profiles of probability distributions. For the Monte Carlo simulation using these two models, equivalent and alternative expressions are proposed, which make the simulation more effective and efficient.
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Acknowledgments
The first author thanks the support from National Natural Science Foundation of China under Key Grant No. 10932009, No. 11072212, and No. 11272279. The second author contributes to this work during his stay at Zhejiang University as a visiting professor. The financial support from Zhejiang University is greatly acknowledged.
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Zhu, W.Q., Cai, G.Q. (2013). On Bounded Stochastic Processes. In: d'Onofrio, A. (eds) Bounded Noises in Physics, Biology, and Engineering. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-7385-5_1
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