Continuous Time Approximations to GARCH(1, 1)-Family Models and Their Limiting Properties

Continuous Time Approximations to GARCH and Stochastic Volatility Models

We collect some continuous time GARCH models and report on how they approximate discrete time GARCH processes. Similarly, certain continuous time volatility models are viewed as approximations to discrete time volatility models. 1 Stochastic volatility models and discrete GARCH Both stochastic volatility models and GARCH processes are popular models for the description of financial time series....

Exponential Models: Approximations for Probabilities

Welch & Peers (1963) used a root-information prior to obtain posterior probabilities for a scalar parameter exponential model and showed that these Bayes probabilities had the confidence property to second order asymptotically. An important undercurrent of this indicates that the constant information reparameterization provides location model structure, for which the confidence property ...

architecture and engineering of nanoscale sculptured thin films and determination of their properties

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Approximations ofthe Limiting

Particle Approximations to the Filtering Problem in Continuous Time

In this chapter, we survey some recent results on the particle system approximations to stochastic filtering problems in continuous time. First, a weighted particle system representation of the optimal filter is given and a numerical scheme based on this representation is proposed. Its convergence to the optimal filter, together with the rate of convergence is proved. Secondly, to reduce the es...