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Stochastic Processes
In this chapter, we introduce a mathematical framework, stochastic processes, which is used to describe small stochastic systems.
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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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Quantum mechanics from stochastic processes
We construct an explicit one-to-one correspondence between non-relativistic stochastic processes and solutions of the Schrödinger equation and...
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Optimal Control of Stochastic Processes
Many control problems appearing for complex systems are subject to imperfectly known disturbances. As we have learned in the previous chapter, these...
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Stochastic Processes in Continuous Space
In this chapter, we consider a stochastic particle in continuous space. A prominent example is a Brownian particle, which is briefly explained at the...
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Optimality and Complexity in Measured Quantum-State Stochastic Processes
If an experimentalist observes a sequence of emitted quantum states via either projective or positive-operator-valued measurements, the outcomes form...
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A stochastic susceptible-infected-susceptible epidemic model with Stratonovich processes
We investigate the susceptible-infected-susceptible (SIS) epidemic model under fluctuating random environments. We consider the effect of uncertainty...
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A novel stochastic photo-thermoelasticity model according to a diffusion interaction processes of excited semiconductor medium
A novel technique under the impact of stochastic heating due to the thermal effect of photothermal theory is investigated. Realistically, stochastic...
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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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Stochastic Thermodynamics
In this chapter, we demonstrate how thermodynamics is implemented in stochastic Markov processes.
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A Solvable Stochastic Model for One-Dimensional Fracturing or Catalysis Processes
We study a model defined on a one-dimensional lattice connected to reservoirs, with diffusive and evaporation/deposition processes depending on three...
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Equation for the Probability of Quantum Transitions in the Method of Path Integrals and Stochastic Processes in the Space of Joint Events
AbstractThe evolution of the system is described as a stochastic process in the space of random joint events, in which both a symmetric difference...
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Stochastic and corpuscular theory of (polarized) light
Both the corpuscular theory of light and the theory of stochastic processes are well known in the literature. However, they are not systematically...
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Quantum-enhanced analysis of discrete stochastic processes
Discrete stochastic processes (DSP) are instrumental for modeling the dynamics of probabilistic systems and have a wide spectrum of applications in...
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Diffusion with Stochastic Resetting
The stochastic resetting processes, whereby the position of the particle is reset to a fixed location at a random sequence of times, are frequently...
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Stochastic Mechanics The Unification of Quantum Mechanics with Brownian Motion
Stochastic mechanics is a theory that holds great promise in resolving the mathematical and interpretational issues encountered in the canonical and...
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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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Robustness of steady state and stochastic cyclicity in generalized coalescence-fragmentation models
AbstractProcesses of coalescence and fragmentation are used to understand the time-evolution of the mass distribution of various systems and may...
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Multiple stochastic resonances and inverse stochastic resonances in asymmetric bistable system under the ultra-high frequency excitation
Ultra-high frequency linear frequency modulation (UHF-LFM) signal, as a kind of typical non-stationary signal, has been widely used in microwave...
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Central Limit Theorems and Moderate Deviations for Stochastic Reaction-Diffusion Lattice Systems
This paper is concerned with the stochastic reaction-diffusion lattice systems defined on the entire set with both locally Lipschitz nonlinear drift...