Multiplicative linear search for a brownian target motion

Second-order stochastic leapfrog algorithm for multiplicative noise brownian motion

A stochastic leapfrog algorithm for the numerical integration of Brownian motion stochastic differential equations with multiplicative noise is proposed and tested. The algorithm has a second-order convergence of moments in a finite time interval and requires the sampling of only one uniformly distributed random variable per time step. The noise may be white or colored. We apply the algorithm t...

Multiplicative Functional for Reflected Brownian Motion via Deterministic Ode

We prove that a sequence of semi-discrete approximations converges to a multiplicative functional for reflected Brownian motion, which intuitively represents the Lyapunov exponent for the corresponding stochastic flow. The method of proof is based on a study of the deterministic version of the problem and the excursion theory.

Adaptive search area for fast motion estimation

In this paper a new method for determining the search area for motion estimation algorithm based on block matching is suggested. In the proposed method the search area is adaptively found for each block of a frame. This search area is similar to that of the full search (FS) algorithm but smaller for most blocks of a frame. Therefore, the proposed algorithm is analogous to FS in terms of reg...

First passage time for Brownian motion and piecewise linear boundaries

We propose a new approach to calculating the first passage time densities for Brownian motion crossing piecewise linear boundaries which can be discontinuous. Using this approach we obtain explicit formulas for the first passage densities and show that they are continuously differentiable except at the break points of the boundaries. Furthermore, these formulas can be used to approximate the fi...

Filtering for Linear Systems Driven by Fractional Brownian Motion