In non-classical limit processes we aim at a better understanding of the family of stochastic processes that can appear as limits under space-time scaling of strongly dependent models encountered in stochastic finance and teletraffic theory. The presence of strong dependence implies that the limiting process is non-classical in the sense of not being a semi-martingale. Some newly found members in this family include fractional Brownian motion, the Poisson bridge and the so-called telecom process, the properties of which are not yet well understood. Our goal is to characterize the domain of attraction for the non-classical limits and study their statistical properties. In stochastic finance we aim at modelling asymmetric information in pricing models. This is an important topic both mathematically and practically. A Bayesian approach to this key area will be developed and statistical tests to detect insider trading will be developed. The application of the Bayesian approach is also numerically challenging.
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