# Project Summary

News: Workshop on Mathematics *" PDEs and Stochastic Processes"* - Transilvania University of Brasov, November 10, 2012

- Project title: Stochastic Analysis and Parameter Estimation in Systems with memory
- Project code: PNII-ID-PCCE-2011-2-0015 / No. 3702/7.05.2012
- Project coordinator: Bucharest Academy of Economic Studies
- Project director: Ciprian Tudor
- Partner institution of the project:
- Institution code: 32
- Institution name: Transilvania University of Brasov
- Faculty: Faculty of Mathematics and Computer Science
- Title: Associate Professor
- Address: Str. Iuliu Maniu Nr. 50, Brasov, Jud. Brasov, Cod 500091
- Phone/Fax: (0268) 414 016

- Personal data of project's coordinator at the partner institution:
- Name: Mihai - Nicolae PASCU
- Academic title: Conferentiar
- Doctor since: 2001
- Ph. D. coordinator: No
- Keywords: stochastic calculus, Malliavin calculus, long -memory processes, homogenization of stochastic equations, local times, parameter estimation.
- Project's classification:
- Domains: PE: Mathematics, Physical sciences, Information and Communication
- Subdomains: PE1: Mathematical foundation: all area of mathematics, pure and applied
- Main research area: PE1_13: Probability and Statistics
- Secondary research area: Stochastic calculus

- Project's duration: 3 years
- Project summary:

We propose a three-year research program on the Gaussian analysis, its applications and its interactions to other branches of mathematics (statistics, wavelet theory or numerical analysis).

More specifically, we wish to develop new analytical methods of stochastic calculus, and at the same time, we would like to apply our results in several domains, as for instance the statistics of stochastic processes and financial mathematics. We will explain our theoretical ideas that we will strongly believe that can be applied to practical aspects such as internet traffic analysis, medical sciences or financial markets.

Stochastic calculus with respect to the standard Brownian motion or more generally with respect to semi-martingales is at the present time one of the essential components of international research in probability theory. The applications of this theory largely exceed, at the present day, the original probabilistic framework and have repercussions in various fields like differential geometry, differential partial equations, theoretical physic, modeling of the financial markets, hydrology or telecommunications. But nowadays, one needs more and more elaborated models to describe the physical phenomena. Sometimes it is necessary to use more general stochastic processes, even non-Gaussian processes, as models in practice. A good class of stochastic processes often used to study practical aspects is the class of so called self similar process, that also exhibit long range dependence (or long memory) . They are used in different domains, such as telecommunications (the internet traffic is mainly self similar), hydrology, economics (the presence of the self similarity in the asset prices have been observed in empirical data), and medical sciences (the detection of the osteoporosis from X-ray images). Our project is articulated around the stochastic analysis for such processes with memory and their applications.