Continuous Time Perpetuities and the Time Reversal of Diffusions

An Improved Time-Reversal-Based Target Localization for Through-Wall Microwave Imaging

Recently, time reversal (TR) method, due to its high functionality in heterogeneous media has been widely employed in microwave imaging (MI) applications. One of the applications turning into a great interest is through-wall microwave imaging (TWMI). In this paper, TR method is applied to detect and localize a target obscured by a brick wall using a numerically generated data. Regarding this, i...

On distributional properties of perpetuities

We study probability distributions of convergent random series of a special structure, called perpetuities. By giving a new argument, we prove that such distributions are of pure type: degenerate, absolutely continuous, or continuously singular. We further provide necessary and sufficient criteria for the finiteness of p-moments, p > 0 as well as exponential moments. In particular, a formula fo...

Photoacoustic image reconstruction of melanoma in skin tissue using time reversal method

This article has no abstract.

Time reversal for drifted fractional Brownian motion with Hurst index H > 1/2

Let X be a drifted fractional Brownian motion with Hurst index H > 1/2. We prove that there exists a fractional backward representation of X , i.e. the time reversed process is a drifted fractional Brownian motion, which continuously extends the one obtained in the theory of time reversal of Brownian diffusions when H = 1/2. We then apply our result to stochastic differential equations driven b...

Quenching Time for a Nonlocal Diffusion Problem with Large Initial Data