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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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Stochastic state-transition-change process and particle physics
The description of particle phenomena is important for basically all fields of physics. The contemporary theoretical statistical description of a...
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Itô versus Stratonovich in a stochastic cosmological model
In this work, we study a stochastic version of the Friedmann acceleration equation. This model has been proposed in the cosmology literature as a...
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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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Effect of fractional-dam** and multiplicative colored noise on stochastic resonance for a second-order nonlinear system
The stochastic resonance (SR) phenomenon for a second-order fractional-dam** nonlinear system driven by multiplicative colored noise and additive...
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Stochastic quantization on Lorentzian manifolds
We embed Nelson’s theory of stochastic quantization in the Schwartz-Meyer second order geometry framework. The result is a non-perturbative theory of...
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Stochastic wave solutions of fractional Radhakrishnan–Kundu–Lakshmanan equation arising in optical fibers with their sensitivity analysis
In this paper, the stochastic fractional Radhakrishnan–Kundu–Lakshmanan equation (SFRKLE) with Kerr law nonlinearity is studied, which is one of the...
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Mathematical study of the dynamics of lymphatic filariasis infection via fractional-calculus
The infection of lymphatic filariasis (LF) is the primary cause of poverty and disability in individuals living with the disease. Many organizations...
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Relativistic Stochastic Mechanics II: Reduced Fokker-Planck Equation in Curved Spacetime
The general covariant Fokker-Planck equations associated with the two different versions of covariant Langevin equation in Part I of this series of...
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Time Series Path Integral Expansions for Stochastic Processes
A form of time series path integral expansion is provided that enables both analytic and numerical temporal effect calculations for a range of...
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On the Size of Chaos via Glauber Calculus in the Classical Mean-Field Dynamics
We consider a system of classical particles, interacting via a smooth, long-range potential, in the mean-field regime, and we optimally analyze the...
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Impact of information intervention on stochastic hepatitis B model and its variable-order fractional network
This paper aims at analyzing the dynamical behavior of a SIR hepatitis B epidemic stochastic model via a novel approach by incorporating the effect...
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Stochastic resonance for a fractional linear oscillator with memory-inertia and memory-dam** kernels subject to dichotomous time-modulated noise
Stochastic resonance (SR) phenomenon for a fractional linear oscillator with memory-inertia and memory-dam** kernels subject to multiplicative...
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Dissipative Solutions to the Stochastic Euler Equations
We study the three-dimensional incompressible Euler equations subject to stochastic forcing. We develop a concept of dissipative martingale...
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Brownian Particle in the Curl of 2-D Stochastic Heat Equations
We study the long time behaviour of a Brownian particle evolving in a dynamic random environment. Recently, Cannizzaro et al. (Ann Probab...
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A stochastic discrete-time co-evolution model and its application in simulating the impacts of behavior changes on the secondary and multiple outbreaks of the COVID-19 pandemic
In this paper, we propose a new stochastic discrete-time multi-scale model to quantify the co-evolution of behavior changes and COVID-19. In this...
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An Outline of Stochastic Calculus
For simplicity again, in this chapter we will only consider processes with just one component. We already remarked in the Sect. 6.3 that a white...
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Exploring stochastic dynamics with different wave structures for the Nizhnik–Novikov–Veselov system and their applications
The article is focused on the analysis of a mathematical model known as the Nizhnik–Novikov–Veselov (SNNV) system, which incorporates a specialized...
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The Global Existence and Averaging Theorem for the Strong Solution of the Stochastic Boussinesq Equations with the Low Froude Number
Considering the stochastic Boussinesq equations with additive noise, we prove the global existence for the strong solution in the case of strong...