Stochastic Processes and Partial Differential Equations in Industry

Dear Colleagues,

In recent decades, stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) have developed rapidly in both theory and application, and have been widely applied to Queuing Theory, Engineering Cybernetics, Information Theory, Financial Engineering, Measurement Control Technology, Management Science, etc. More recently, SDEs and SPDEs have entered in the research of machine learning, for instance, many stochastic algorithms such as stochastic gradient descent (SGD) and stochastic variance reduced gradient converge to SDEs or delayed SDEs. Many stochastic methods in machine learning need tools in SDEs and SPDEs, for instance, Lyapunov function method and coupling method have become popular in analysing the convergence of stochastic algorithms.  With the help of stochastic dynamical system theory, the higher-order parabolic SPDEs are widely used in the field of material science. Furthermore, the fractional SDEs and and SPDEs have received much attention, they have been applied to model various phenomena in risk management, statistical mechanics, electromagnetics and quantum mechanics, etc.

All theoretical and applied works on the above-presented stochastic processes and stochastic partial differential equations are available in the Special Issue.

We are pleased to invite you to submit your recent work to the Special Issue, which focuses on solving industrial problems with stochastic processes and partial differential equation.

This Special Issue aims to promote the development of the relevant theories of stochastic processes and stochastic partial differential equations, advocate the application of relevant theories to practice, and promote the application of stochastic processes and partial differential equations in industry.

In this Special Issue, original research articles and reviews are welcome. Research areas may include (but not limited to) the following:

• stochastic processes and partial differential equations in industry.

I look forward to receiving your contributions.

Dr. Lihu Xu
Dr. Peng Chen
Dr. Jianya Lu
Guest Editors

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• stochastic processes
• stochastic partial differential equations
• stochastic dynamics systems theory and applications
• model phenomena in industry
• queuing theory