Statistical Analysis of Curved Probability Densities

analysis of ruin probability for insurance companies using markov chain

در این پایان نامه نشان داده ایم که چگونه می توان مدل ریسک بیمه ای اسپیرر اندرسون را به کمک زنجیره های مارکوف تعریف کرد. سپس به کمک روش های آنالیز ماتریسی احتمال برشکستگی ، میزان مازاد در هنگام برشکستگی و میزان کسری بودجه در زمان وقوع برشکستگی را محاسبه کرده ایم. هدف ما در این پایان نامه بسیار محاسباتی و کاربردی تر از روش های است که در گذشته برای محاسبه این احتمال ارائه شده است. در ابتدا ما نشا...

Probability Densities for Some One-Dimensional Problems in Statistical Mechanics

Regularly varying probability densities

The convolution of regularly varying probability densities is proved asymptotic to their sum, and hence is also regularly varying. Extensions to rapid variation, O-regular variation, and other types of asymptotic decay are also given. Regularly varying distribution functions have long been used in probability theory; see e.g. Feller [7, VIII.8], Bingham, Goldie and Teugels [5, Ch. 8]. This note...

Chaos for Liouville probability densities.

Using the method of symbolic dynamics, we show that a large class of classical chaotic maps exhibit exponential hypersensitivity to perturbation, i.e., a rapid increase with time of the information needed to describe the perturbed time evolution of the Liouville density, the information attaining values that are exponentially larger than the entropy increase that results from averaging over the...

Probability Densities in Strong Turbulence

According to modern developments in turbulence theory, the ”dissipation” scales (u.v. cut-offs) η form a random field related to velocity increments δηu. In this work we, using Mellin’s transform combined with the Gaussain large -scale boundary condition, calculate probability densities (PDFs) of velocity increments P (δru, r) and the PDF of the dissipation scales Q(η,Re), where Re is the large...