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A two state model for noise-induced resonance in bistable systems with delay

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Author Info
Markus Fischer
Peter Imkeller
Abstract

The subject of the present paper is a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise exhibits a phenomenon similar to what is known as stochastic resonance. The reference model is given by a one dimensional parametrized stochastic differential equation with point delay, basic properties whereof we check. With a view to capturing the effective dynamics and, in particular, the resonance-like behaviour of the reference model we construct a simplified or reduced model, the two state model, first in discrete time, then in the limit of discrete time tending to continuous time. The main advantage of the reduced model is that it enables us to explicitly calculate the distribution of residence times which in turn can be used to characterize the phenomenon of noise-induced resonance. Drawing on what has been proposed in the physics literature, we outline a heuristic method for establishing the link between the two state model and the reference model. The resonance characteristics developed for the reduced model can thus be applied to the original model.

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Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2005-017.

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Length: 45 pages
Date of creation: Mar 2005
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Handle: RePEc:hum:wpaper:sfb649dp2005-017

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Related research
Keywords: logit model utility maximization nested logit non-normalized nested logit simulation study

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software
M31 - Business Administration and Business Economics; Marketing; Accounting - - Marketing and Advertising - - - Marketing

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Szymon Borak & Kai Detlefsen & Wolfgang Härdle, 2005. "FFT Based Option Pricing," SFB 649 Discussion Papers SFB649DP2005-011, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  2. Ralf Brüggemann & Carsten Trenkler, 2005. "Are Eastern European Countries Catching Up? Time Series Evidence for Czech Republic, Hungary, and Poland," SFB 649 Discussion Papers SFB649DP2005-014, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  3. Enzo Giacomini & Wolfgang Härdle, 2005. "Value-at-Risk Calculations with Time Varying Copulae," SFB 649 Discussion Papers SFB649DP2005-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  4. Dirk Krueger & Harald Uhlig, 2005. "Competitive Risk Sharing Contracts with One-Sided Commitment," CFS Working Paper Series 2005/07, Center for Financial Studies. [Downloadable!]
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  5. Szymon Borak & Wolfgang Härdle & Rafal Weron, 2005. "Stable Distributions," SFB 649 Discussion Papers SFB649DP2005-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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