Newton Revisited: An excursion in Euclidean geometry
An interpretation of selected parts of Newton's Principia, with modern notation and methods. Keplers Laws are derived from an inverse square law using Newton's methods.
math.HO↗
arXiv subjects
Greg Markowsky
Publications and source records attributed to Greg Markowsky.
Renormalization and convergence in law for the derivative of intersection local time in R^2
In this paper we will examine the derivative of intersection local time of Brownian motion and symmetric stable processes in $R^2$. These processes do not exist when defined in the canonical way. The purpose of this paper is to exhibit the correct rate for renormaliztion of these processes.
math.PR↗
A Tanaka formula for the derivative of intersection local time in $\reals^1$
Let $B_t$ be a one dimensional Brownian motion, and let $α'$ denote the derivative of the intersection local time of $B_t$ as defined in Jay Rosen's work (see references). The object of this paper is to prove the following formula $(1/2)α'_t(x) + (1/2)sgn(x)t = \int_0^t L_s^{B_s - x}dB_s - \int_0^t sgn(B_t - B_u - x) du$ which was given as a formal identity by Rosen without proof.
math.PR↗