TFR Predictions Based on Brownian Motion Theory

Potential Theory of Subordinate Brownian Motion

Classical Potential Theory and Brownian Motion

Pioneering work of Doob, Kac, and Kakutani showed that there was a beautiful and deep connection between certain problems in the study of Brownian motion and those of classical potential theory. This work stimulated much research on the theory of Markov processes. In spite of all this work, however, there doesn't appear anywhere in the literature any reasonably complete treatment of the connect...

Limiting Behaviors for Brownian Motion Reflected on Brownian Motion

Suppose that g(t) and Wt are independent Brownian motions starting from g(0) = W0 = 0. Consider the Brownian motion Yt reflected on g(t), obtained from Wt by the means of the Skorohod lemma. The upper and lower limiting behaviors of Yt are presented. The upper tail estimate on exit time is computed via principal eigenvalue.

on Brownian Motion

We present an introduction to Brownian motion, an important continuous-time stochastic process that serves as a continuous-time analog to the simple symmetric random walk on the one hand, and shares fundamental properties with the Poisson counting process on the other hand. Throughout, we use the following notation for the real numbers, the non-negative real numbers, the integers, and the non-n...

Notes on Brownian Motion