Karl Sigman 1 Simulating normal ( Gaussian ) rvs with applications to simu - lating

Karl Sigman 1 Simulating normal ( Gaussian ) rvs with applications to simu - lating Brownian motion and geometric Brownian motion in one and two dimensions

Fundamental to many applications in financial engineering is the normal (Gaussian) distribution. It is the building block for simulating such basic stochastic processes as Brownian motion and geometric Brownian motion. In this section, we will go over algorithms for generating univariate normal rvs and learn how to use such algorithms for constructing sample paths of Brownian motion and geometr...

Simulating Brownian motion ( BM ) and geometric Brownian

2) and 3) together can be summarized by: If t0 = 0 < t1 < t2 < · · · < tk, then the increment rvs B(ti) − B(ti−1), i ∈ {1, . . . k}, are independent with B(ti) − B(ti−1) ∼ N(0, ti − ti−1) (normal with mean 0 and variance ti − ti−1). In particular, B(ti) − B(ti−1) is independent of B(ti−1) = B(ti−1)−B(0). If we only wish to simulate B(t) at one fixed value t, then we need only generate a unit no...

A Novel Conformal End-fire Antenna Design Using the Competitive Algorithm of Simu- Lating Natural Tree Growth

This paper presents a novel conformal end-fire antenna whose design employs the Competitive Algorithm of Simulating Natural Tree Growth. This algorithm is based on the idea of simulating the processes of growth and wilting of natural trees and can search from simple to complicated structures with rapid convergence. Four optimized radiation elements were designed on a cross structure to verify t...

Menge: A Modular Framework for Simu- lating Crowd Movement

We present Menge, a cross-platform, extensible, modular framework for sim1 ulating pedestrian movement in a crowd. Menge’s architecture is inspired by an implicit 2 decomposition of the problem of simulating crowds into component subproblems. These 3 subproblems can typically be solved in many ways; different combinations of subproblem 4 solutions yield crowd simulators with likewise varying pr...

Sigman 1 Geometric Brownian motion