Paul M. Geffert analyses the interplay of noise and time delay in non-excitable nonlinear systems and the modulation of stochastic effects. In particular, the author studies coherence resonance, which is a constructive effect of noise that occurs in nonlinear systems, and demonstrates that it can be modulated by time-delayed feedback. Analytical methods for the investigation of stochastic delay…
This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of small and large networks of interconnected neurons. The necessary neuroscience background to these p…
This book covers recent developments in the non-standard asymptotics of the mathematical narrow escape problem in stochastic theory, as well as applications of the narrow escape problem in cell biology. The first part of the book concentrates on mathematical methods, including advanced asymptotic methods in partial equations, and is aimed primarily at applied mathematicians and theoretical phys…
The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues. There is a growing need to tackle uncertainty in applications of optimization. For example the massive introduction of renewable energies in power systems challenges …
This volume presents papers collected on the occasion of the 12th Workshop on Stochastic Models, Statistics and Their Applications, jointly organized by the Institute of Mathematics and Computer Science of Wrocław University of Technology, the Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, and by the Institute of Statistics of RWTH Aachen Univers…
The Stochastic Equation. The authors of this text (called DB, ED and TM) started their collaboration with the paper Buraczewski et al. [76] in 2011. We studied large deviations and ruin probabilities for the solution ðXtÞ to Kesten’s stochastic recurrence equation
This course concerns the stochastic modeling of population dynamics. In the first part, we focus on monotype populations described by one-dimensional stochastic differential equations with jumps. We consider their scaling limits for large populations and study the long time behavior of the limiting processes. It is achieved, thanks to martingale properties, Poisson measure representations, a…
The assessment of thermal fatigue crack growth due to turbulent mixing of hot and cold coolants presents significant challenges, in particular, to determine the thermal loading spectrum. Thermal striping is defined as a random temperature fluctuation produced by incomplete mixing of fluid streams at different temperatures, and it is essentially a random phenomenon in a temporal sense.
This volume presents the results of Computational Fluid Dynamics (CFD) analysis that can be used for conceptual studies of product design, detail product development, process troubleshooting. It demonstrates the benefit of CFD modeling as a cost saving, timely, safe and easy to scale-up methodology.
The study of stochastic differential equations (SDEs) driven by Lévy processes in R originated in the book by Skorokhod [97]. In view of the Lévy–Itô decomposition, he reduced the problem of studying such SDEs to the analysis of SDEs driven by compensated Poisson random measures (cPrms) and Brownian motion, under a mild restriction [97]. He was aware of the fact that the restriction ca…