Complete analytic solution to Brownian unicycle dynamics

Unbiased rotational moves for rigid-body dynamics.

We introduce an unbiased protocol for performing rotational moves in rigid-body dynamics simulations. This approach-based on the analytic solution for the rotational equations of motion for an orthogonal coordinate system at constant angular velocity-removes deficiencies that have been largely ignored in Brownian dynamics simulations, namely errors for finite rotations that result from applying...

The Effects of Different SDE Calculus on Dynamics of Nano-Aerosols Motion in Two Phase Flow Systems

Langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. The Brownian motion generated from molecular bombardment was taken as a Wiener stochastic process and approximated by a Gaussian white noise. Euler-Maruyama method was used to solve the Langevin equation numerically. The accuracy of Brownian simulation was checked by performing a series of simulati...

An Analytic Method for Solving Uncertain Differential Equations

Uncertain differential equations are a type of differential equations driven by canonical process, and are quite different from stochastic differential equations that are driven by Brownian motion. A solution of an uncertain differential equation is an uncertain process. This paper presents an analytic method to solve a particular class of nonlinear uncertain differential equations and gives so...

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

Why Are Quadratic Normal Volatility Models Analytically Tractable?

We discuss the class of “Quadratic Normal Volatility” (QNV) models, which have drawn much attention in the financial industry due to their analytic tractability and flexibility. We characterize these models as those that can be obtained from stopped Brownian motion by a simple transformation and a change of measure that depends only on the terminal value of the stopped Brownian motion. This exp...