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fbtwitterlinkedinvimeoflicker grey 14rssslideshare1

Statistical estimation and approximation of anomalous diffusion

Title
Statistical estimation and approximation of anomalous diffusion
Funding
ARC | Discovery Projects
Contract (GA) number
DP0345577
Start Date
2003/01/01
End Date
2005/12/31
Open Access mandate
no
Organizations
-
More information
http://purl.org/au-research/grants/arc/DP0345577

 

  • Linear filtering of systems with memory

    We study the linear filtering problem for systems driven by continuous Gaussian processes with memory described by two parameters. The driving processes have the virtue that they possess stationary increments and simple semimartingale representations simultaneously. It allows for straightforward parameter estimations. After giving the semimartingale representations of the processes by innovation theory, we derive Kalman-Bucy-type filtering equations for the systems. We apply the result to the...

    Binary market models with memory

    We construct a binary market model with memory that approximates a continuous-time market model driven by a Gaussian process equivalent to Brownian motion. We give a sufficient conditions for the binary market to be arbitrage-free. In a case when arbitrage opportunities exist, we present the rate at which the arbitrage probability tends to zero as the number of periods goes to infinity.
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