On Strong Binomial Approximation for Stochastic Processes and Applications for Financial Modelling

strong approximation for itô stochastic differential equations

in this paper, a class of semi-implicit two-stage stochastic runge-kutta methods (srks) of strong global order one, with minimum principal error constants are given. these methods are applied to solve itô stochastic differential equations (sdes) with a wiener process. the efficiency of this method with respect to explicit two-stage itô runge-kutta methods (irks), it method, milstien method, sem...

tight frame approximation for multi-frames and super-frames

در این پایان نامه یک مولد برای چند قاب یا ابر قاب تولید شده تحت عمل نمایش یکانی تصویر برای گروه های شمارش پذیر گسسته بررسی خواهد شد. مثال هایی از این قاب ها چند قاب های گابور، ابرقاب های گابور و قاب هایی برای زیرفضاهای انتقال پایاست. نشان می دهیم که مولد چند قاب تنک نرمال شده (ابرقاب) یکتا وجود دارد به طوری که مینیمم فاصله را از ان دارد. همچنین مسایل مشابه برای قاب های دوگان مطرح شده و برخی ...

Stochastic approximation for background modelling

Many background modelling approaches are based on mixtures of multivariate Gaussians with diagonal covariance matrices. This often yields good results, but complex backgrounds are not adequately captured, and postprocessing techniques are needed. Here we propose the use of mixtures of uniform distributions and multivariate Gaussians with full covariance matrices. These mixtures are able to cope...

Strong approximation of stochastic processes using random walks

Stochastic Multiplicative Processes for Financial Markets

We study a stochastic multiplicative system composed of finite asynchronous elements to describe the wealth evolution in financial markets. We find that the wealth fluctuations or returns of this system can be described by a walk with correlated step sizes obeying truncated Lévy-like distribution, and the cross-correlation between relative updated wealths is the origin of the nontrivial propert...