$\varepsilon$-Strong simulation of the Brownian path

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...

The Strong Markov Property of the Brownian Motion

Sample Path Properties of Bifractional Brownian Motion

Let B = { B(t), t ∈ R+ } be a bifractional Brownian motion in R. We prove that B is strongly locally nondeterministic. Applying this property and a stochastic integral representation of B , we establish Chung’s law of the iterated logarithm for B , as well as sharp Hölder conditions and tail probability estimates for the local times of B . We also consider the existence and the regularity of th...

Some Path Properties of Iterated Brownian Motion

We will consider the process {Z(t) df = X(Y (t)), t ≥ 0} which we will call “iterated Brownian motion” or simply IBM. Funaki (1979) proved that a similar process is related to “squared Laplacian.” Krylov (1960) and Hochberg (1978) considered finitely additive signed measures on the path space corresponding to squared Laplacian (there exists a genuine probabilistic approach, see, e.g., Ma̧drecki ...