Stochastic Calculus for Fractional Brownian Motion
A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Probability and Statistics".
Deadline for manuscript submissions: closed (30 June 2022) | Viewed by 5116
Special Issue Editors
Interests: stochastic processes; stochastic analysis and stochastic differential equations; fractional processes; their financial and statistical applications
Special Issues, Collections and Topics in MDPI journals
Interests: fractional and multifractional stochastic processes and fields; stochastic differential equations (ordinary and partial); statistical inference for stochastic processes
Special Issue Information
Dear colleagues,
The aim of this issue is to present the modern issues that connect fractality and fractionality. The self-similarity phenomena, or fractal phenomena, are being actively investigated by various research groups throughout the world. The reason of such profound interest to these phenomena is their ubiquity in different areas. Fractal behavior can appear statically, in which case it is usually referred to as fractality, or dynamically, in which case it is called fractionality. Statically, fractals appear both in natural sciences, such as geophysics, crystallography, astronomy, biology, chemistry, bioinformatics, and in different branches of mathematics: number theory, geometry, theory of differential equations, etc. Dynamically, fractal behavior is demonstrated by macroscopic collections of the units that are endowed with the potential to evolve in time. Such collections are objects of study in fluid mechanics, physics of nano-particles, electronics, cellular communications, economics, financial mathematics, and many other areas. Because of its static nature, the word “fractality” is more common when speaking of deterministic objects, while “fractionality” often means stochastic behavior. Modern concepts of multifractality and multifractionality are further extensions of these notions. They are used to describe the phenomena which are only locally self-similar. One of the important mathematical tools to investigate fractality and fractionality is fractional calculus. Statistical inference for fractional and related models is a rapidly developing area of research, which is highly important for practical applications. To connect these issues, we propose the following topics:
- fractional calculus
- fractional equations and fractional dynamics
- fractional stochastic analysis
- fractional and multifractional stochastic processes
- applications of fractal and fractional analysis
- SPDE with fractional processes
- statistics of fractional models
We wish to present the mutual ways how to deal with complicated dynamical systems with fractal properties and long-range dependence both from the point of view of fractal differential equations and fractional stochastic differential equations, both from the point of view of the finite-dimensional distributions and from the point of view of the behavior of their trajectories. The main goal of the Special Issue is to unite and unify these two approaches—the distributional approach and the approach from the point of view of the trajectories of the complicated dynamical non-Markovian system. Special attention is paid to statistical applications of fractional models.
Prof. Dr. Yuliya Mishura
Dr. Kostiantyn Ralchenko
Guest Editors
Manuscript Submission Information
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