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Optimal Total Variation Bounds for Stochastic Differential Delay Equations with Small Noises
In this paper, we study the central limit theorem for the solutions of stochastic differential delay equations with small noises. Our aim is to...
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Periodic Solutions in Distribution of Mean-Field Stochastic Differential Equations
In this paper, we study periodic solutions in distribution of mean-field stochastic differential equations. We introduce the notion of upper and...
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Propagation of Chaos for Weakly Interacting Mild Solutions to Stochastic Partial Differential Equations
This article investigates the propagation of chaos property for weakly interacting mild solutions to semilinear stochastic partial differential...
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Dynamics of stochastic nonlocal partial differential equations
This paper is concerned with the asymptotic behavior of solutions to nonlocal stochastic partial differential equations with multiplicative and...
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Equivalence of measures and stochastic equations of hydrodynamic theory of plasma
Stochastic equations of hydrodynamic theory of plasma are presened. The article shows that for transfer processes in liquid and gas, on the one hand,...
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Non-parametric Estimation of Stochastic Differential Equations from Stationary Time-Series
We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary...
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Euler–Lagrangian Approach to Stochastic Euler Equations in Sobolev Spaces
The purpose of this paper is to establish the equivalence between Lagrangian and classical formulations for the stochastic incompressible Euler...
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Stern–Gerlach, EPRB and Bell Inequalities: An Analysis Using the Quantum Hamilton Equations of Stochastic Mechanics
The discussion of the recently derived quantum Hamilton equations for a spinning particle is extended to spin measurement in a Stern–Gerlach...
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Stochastic Navier–Stokes Equations for Turbulent Flows in Critical Spaces
In this paper we study the stochastic Navier–Stokes equations on the d -dimensional torus with transport noise, which arise in the study of turbulent...
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A Consistent Stochastic Large-Scale Representation of the Navier–Stokes Equations
In this paper we analyze the theoretical properties of a stochastic representation of the incompressible Navier–Stokes equations defined in the...
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Comprehensive soliton solutions of fractional stochastic Kraenkel–Manna–Merle equations in ferromagnetic materials
The inner characteristics of numerous nonlinear phenomena that arise in real-life problems are stated through nonlinear partial differential...
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Stochastic Dynamics on \(\mathbb {R}^d\)
This chapter discusses the theory of Brownian motion (Wiener process) with drift in detail. It derives the stochastic differential equations of...
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Averaging Principles for Stochastic 2D Navier–Stokes Equations
In this paper, we will establish two kinds of averaging principles for stochastic 2D Navier–Stokes equations, i.e. Bogoliubov averaging principle and...
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Stochastic Approach to Population Dynamics
We analyze a stochastic approach to population dynamics in which the number of individuals in each class is treated as a stochastic variable. The...
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Exploring soliton solutions of stochastic Phi-4 equation through extended Sinh-Gordon expansion method
Numerous systems and phenomena that appear to fluctuate randomly are mathematically modeled using stochastic processes. In this paper stochastic...
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Exact solutions of nonlinear stochastic Newell-Whitehead-Segel equation by a reduction technique
The Newell-Whitehead-Segel (NWS) model is a reaction-diffusion system that has been widely used to study pattern formation in biological and physical...
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Existence and Uniqueness of Solutions to Backward 2D and 3D Stochastic Convective Brinkman–Forchheimer Equations Forced by Lévy Noise
The two- and three-dimensional incompressible backward stochastic convective Brinkman–Forchheimer (BSCBF) equations on a torus driven by Lévy noise...
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Stochastic Processes
In this chapter, we lay the foundation of stochastic processes. We start with a general definition of a stochastic process, and then specialize to...
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RG Method Applied to Stochastic Equations
The RG method is applied to a derivation of the Fokker-Planck equations and its adiabatic reduction for the system with fast and slow variables as...