On Comparison Results for Neutral Stochastic Differential Equations of Reaction-Diffusion Type in L2(ℝd)

Abstract

Springer Complexity is an interdisciplinary program publishing the best research and academic-level teaching on both fundamental and applied aspects of complex systemscutting across all traditional disciplines of the natural and life sciences, engineering, economics, medicine, neuroscience, social and computer science.Complex Systems are systems that comprise many interacting parts with the ability to generate a new quality of macroscopic collective behavior the manifestations of which are the spontaneous formation of distinctive temporal, spatial or functional structures. Models of such systems can be successfully mapped onto quite diverse "real-life" situations like the climate, the coherent emission of light from lasers, chemical reaction-diffusion systems, biological cellular networks, the dynamics of stock markets and of the internet, earthquake statistics and prediction, freeway traffic, the human brain, or the formation of opinions in social systems, to name just some of the popular applications.Although their scope and methodologies overlap somewhat, one can distinguish the following main concepts and tools: self-organization, nonlinear dynamics, synergetics, turbulence, dynamical systems, catastrophes, instabilities, stochastic processes, chaos, graphs and networks, cellular automata, adaptive systems, genetic algorithms and computational intelligence.The three major book publication platforms of the Springer Complexity program are the monograph series "Understanding Complex Systems" focusing on the various applications of complexity, the "Springer Series in Synergetics", which is devoted to the quantitative theoretical and methodological foundations, and the "SpringerBriefs in Complexity" which are concise and topical working reports, case-studies, surveys, essays and lecture notes of relevance to the field. In addition to the books in these two core series, the program also incorporates individual titles ranging from textbooks to major reference works.

Invariant measure for neutral stochastic functional differential equations with non-Lipschitz coefficients

“…These properties were established for (1) in [14] in case when A is Laplacian. The analog of comparison theorem for such equations was established in [30].…”

On Weak and Strong Solutions of Paired Stochastic Functional Differential Equations in Infinite-Dimensional Spaces

“…The work [4] is devoted to the existence of weak solutions. Similar equations of neutral type have been studied in [5], [6], [7], [8], [9], where the questions of controllability and the Markovian property have been considered and comparison theorems have been obtained. In [10], using the compactness approach [11] the authors establish the existence of an invariant measure.…”

Invariant Measure for Neutral Stochastic Functional Differential Equations with Non-Lipschitz Coefficients

“…These properties were established for (1) in [14] in case when A is Laplacian. The analog of comparison theorem for such equations was established in [30].…”