We solve multidimensional SDEs with distributional drift driven by symmetric, ?-stable Lévy processes for ??(1,2] studying the associated (singular) martingale problem and solving Kolmogorov backward equation. allow drifts of regularity (2?2?)?3, in particular we go beyond now well understood “Young regime”, where must have better than (1??)?2. The analysis equation low regime is based on parac...

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We formulate and prove a local stable manifold theorem for stochastic differential equations (SDEs) that are driven by spatial Kunita-type semimartingales with stationary ergodic increments. Both Stratonovich and Itôtype equations are treated. Starting with the existence of a stochastic flow for a SDE, we introduce the notion of a hyperbolic stationary trajectory. We prove the existence of inva...

1. INTRODUCTION This paper is my description of the state of statistical data editing and current research problems. It is not intended to be a complete description of all areas. Rather, it represents sub-areas of statistical data editing that I will describe in sufficient detail so that the discussion of a few research problems is more easily understood. I define statistical data editing (SDE)...

The monitoring of biofilm development at a small-scale is often observed to be a stochastic process. This raises important issues concerning the reproducibility of biofilm growth monitoring experiments. By realising that there are limits to the latter, a model of biofilm accumulation curves that takes into account the dynamics of seemingly random fluctuations resulting from sloughing events is ...

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...

The Simulation-Driven Engineering (SDE) research project aims to improve real-time embedded system development by integrating the use of modeling and simulation as a fundamental cornerstone in all development stages. Shortterm goals are to simplify the reuse of engineering work products, and to develop a discrete-event based simulation architecture suitable for target products. The long-term go...

We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic variable. The SDE is obtained from the analogy with earlier proposed model of tra...