- Joined
- 4/19/08
- Messages
- 6
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- 11
Hi<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:p></o:p>
I will apply for a PhD position i mathematical statistics with research proposal present bellow.<o:p></o:p>
My goal is to push the research into the financial market. It can be interesting if anyone can give me some proposals of relevant financial topics that I could focus on.<o:p></o:p>
I have a solid background in, mathematical and financial statistics.
Phd Proposal<o:p></o:p>
In the last two decades or so there is observed a steadily growing interest in non- Gaussian modeling as the increasing number of data that exhibit intrinsically non-Gaussian features is reported in various disciplines. Thus for example, stochastic models for water waves that are based on energy spectra lead to the Gaussian character of the sea surface only if they are derived from linear approximations of deterministic surface waves. Higher order approximations leads to different than Gaussian seas such as Lagrangian model for irregular ocean waves. Moreover Gaussian models seem to approximate the sea surface quite well only when the sea conditions are mild and the theory fails for rough seas and specially in the cases when extreme waves are considered. For the planning and safety of marine and other offshore operations, where very rare events has to be taken into account, the linear theory is often not adequate. A serious consequence of not taking this into account in a fatigue application is that the fatigue life predictions from the model may be far too long. In order to overcome this problem a lot of effort has been made to find suitable non-Gaussian models. Similarly in hydrology, classical theories describing velocity intermittency in turbulent flows are assuming log-normal distribution of the velocity dissipation. However, this "assumed distribution" is essentially empirical and recent investigations have shown deviations from lognormality. It is observed in the data sets that logarithms of increment probability produces non-Gaussian behavior at smaller measurement lags and converges to Gaussian behavior at larger lags. Because of this, in recent years, also in this area several non-Gaussian models have been proposed to account for these deviations from classical models. <o:p></o:p>
All this exemplifies the need for other than Gaussian stochastic models and in fact it stimulated active research on alternative distributions and processes. Despite this growing interest in non-Gaussian distributions, more advanced models such as stochastic processes and fields that are derived from these distributions are lagging behind in theoretical development. Most of the efforts for the second order models have taken Gaussian processes as the starting point like in the class of transformed Gaussian processes. Another, and more complex, approach to non-Gaussian processes are obtained by Volterra series expansions which can be described as higher order transformations of Gaussian processes. Through the proposed research another approach to modeling of non-Gaussian second order random signals is proposed. It differs fundamentally from the previous ones in that it goes beyond the Gaussian theory but still, as in the Gaussian case, the main tool for the new model is the spectral theory. The research project sets as a goal to progress the theoretical understanding the Laplace laws based models to the extent that they become not only attractive but also practically usable alternative to Gaussian ones. Parallel to this their applicability to selected problems in engineering and environmental science will be explored. It is strongly believed that the considered models are universal and ultimately they will be used in a wide range of applications. <o:p></o:p>
I will apply for a PhD position i mathematical statistics with research proposal present bellow.<o:p></o:p>
My goal is to push the research into the financial market. It can be interesting if anyone can give me some proposals of relevant financial topics that I could focus on.<o:p></o:p>
I have a solid background in, mathematical and financial statistics.
Phd Proposal<o:p></o:p>
In the last two decades or so there is observed a steadily growing interest in non- Gaussian modeling as the increasing number of data that exhibit intrinsically non-Gaussian features is reported in various disciplines. Thus for example, stochastic models for water waves that are based on energy spectra lead to the Gaussian character of the sea surface only if they are derived from linear approximations of deterministic surface waves. Higher order approximations leads to different than Gaussian seas such as Lagrangian model for irregular ocean waves. Moreover Gaussian models seem to approximate the sea surface quite well only when the sea conditions are mild and the theory fails for rough seas and specially in the cases when extreme waves are considered. For the planning and safety of marine and other offshore operations, where very rare events has to be taken into account, the linear theory is often not adequate. A serious consequence of not taking this into account in a fatigue application is that the fatigue life predictions from the model may be far too long. In order to overcome this problem a lot of effort has been made to find suitable non-Gaussian models. Similarly in hydrology, classical theories describing velocity intermittency in turbulent flows are assuming log-normal distribution of the velocity dissipation. However, this "assumed distribution" is essentially empirical and recent investigations have shown deviations from lognormality. It is observed in the data sets that logarithms of increment probability produces non-Gaussian behavior at smaller measurement lags and converges to Gaussian behavior at larger lags. Because of this, in recent years, also in this area several non-Gaussian models have been proposed to account for these deviations from classical models. <o:p></o:p>
All this exemplifies the need for other than Gaussian stochastic models and in fact it stimulated active research on alternative distributions and processes. Despite this growing interest in non-Gaussian distributions, more advanced models such as stochastic processes and fields that are derived from these distributions are lagging behind in theoretical development. Most of the efforts for the second order models have taken Gaussian processes as the starting point like in the class of transformed Gaussian processes. Another, and more complex, approach to non-Gaussian processes are obtained by Volterra series expansions which can be described as higher order transformations of Gaussian processes. Through the proposed research another approach to modeling of non-Gaussian second order random signals is proposed. It differs fundamentally from the previous ones in that it goes beyond the Gaussian theory but still, as in the Gaussian case, the main tool for the new model is the spectral theory. The research project sets as a goal to progress the theoretical understanding the Laplace laws based models to the extent that they become not only attractive but also practically usable alternative to Gaussian ones. Parallel to this their applicability to selected problems in engineering and environmental science will be explored. It is strongly believed that the considered models are universal and ultimately they will be used in a wide range of applications. <o:p></o:p>