New Trends in Stochastic Processes, Probability and Statistics

Dear Colleagues,

You are cordially invited to contribute to this Special Issue, entitled "New Trends in Stochastic Processes, Probability and Statistics", with an original research article or a comprehensive review paper. The primary focus of this Special Issue is modern areas of the theory of stochastic processes and mathematical statistics. Special attention will be paid to processes that enable us to study the evolution of particle systems in which each particle that is born, dies, and can move through space in different environments follows rules that take into account the random factor. Such processes have applications in a variety of fields, from statistical physics to population dynamics. One of the key issues in the analysis of such systems is the limiting behavior of the various features that describe their evolution. Despite the rigor of the theoretical results, their practical interpretation is required for numerous applications. Moreover, we hope that the manuscripts submitted will be unified by prevalent ideas in the field of branching processes; these include, in particular, controlled random processes, branching random walks in inhomogeneous and random environments, and Markov and non-Markov processes with discrete or continuous time. Currently, the theory surrounding large deviations in such processes is under active development. The development of novel methods for the study of stochastic processes, combining the martingale technique and the spectral approach for the analysis of the spectrum of high-dimensional random matrices, is also a topic we welcome the address of in this Special Issue. Simultaneously, issues pertaining to the modeling and statistical analysis of such systems in various applications might be raised. You are invited to suggest statistical approaches that might be employed to recognize the effect of intermittency on empirical data, and to show that external randomization can enable test statistics to be better approximated due to their limiting distributions. The Special Issue addresses a topic that is a vital aspect of modern applied statistics, because one of the main issues encountered in these studies is the identification of the parameters of random processes and the development of nonparametric statistical methods.

Prof. Dr. Alexander Tikhomirov
Prof. Dr. Vladimir Ulyanov
Prof. Dr. Elena Yarovaya
Guest Editors

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• stochastic processes
• limit theorems
• branching processes
• random walks
• random environments
• branching random walks
• martingales
• spectral methods
• random matrix
• statistical inferences
• regression models
• weighted random sums
• non-asymptotic analysis

• Limit Theorems of Probability Theory in Mathematics (16 articles)