A strong uniform approximation of fractional Brownian motion by means of transport processes

Strong Approximation of Brownian Motion

Simple random walk and Brownian motion are two strongly interconnected mathematical concepts. They are widely involved in not only pure math, but also in many other scientific fields. In this paper I will first introduce and define some basic concepts of discrete-time random walk. Then I will construct Brownian Motion with some basic properties, and use a method called the strong approximation ...

a generalization of strong causality

در این رساله t_n - علیت قوی تعریف می شود. این رده ها در جدول علیت فضا- زمان بین علیت پایدار و علیت قوی قرار دارند. یک قضیه برای رده بندی آنها ثابت می شود و t_n- علیت قوی با رده های علی کارتر مقایسه می شود. همچنین ثابت می شود که علیت فشرده پایدار از t_n - علیت قوی نتیجه می شود. بعلاوه به بررسی رابطه نظریه دامنه ها با نسبیت عام می پردازیم و ثابت می کنیم که نوع خاصی از فضا- زمان های علی پایدار, ب...

Maxima of stochastic processes driven by fractional Brownian motion

We study stationary processes given as solutions to SDEs driven by fractional Brownian motion (FBM). This class includes the fractional Ornstein-Uhlenbeck process (FOUP), but is a much richer class of processes, which can be obtained by state space transformations of the FOUP. An explicit formula in terms of Euler’s Γ-function describes the asymptotic behaviour of the covariance function of FOU...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Fractional Brownian Motion Limit for a Model of Turbulent Transport

Passive scalar motion in a family of random Gaussian velocity fields with longrange correlations is shown to converge to persistent fractional Brownian motions in long times.