A transformed path integral approach for solution of the Fokker–Planck equation

2017 ◽  
Vol 346 ◽  
pp. 49-70 ◽  
Author(s):  
Gnana M. Subramaniam ◽  
Prakash Vedula
Keyword(s):  
Path Integral ◽  
Planck Equation ◽  
Integral Approach ◽  
Path Integral Approach ◽  
Fokker Planck Equation ◽  
Fokker Planck

Simulating Drift-Diffusion Processes With Generalized Interval Probability

2012 ◽  
Author(s):  
Yan Wang
Keyword(s):  
Path Integral ◽  
Stochastic Systems ◽  
Diffusion Processes ◽  
Epistemic Uncertainty ◽  
Planck Equation ◽  
Integral Approach ◽  
Drift Diffusion ◽  
Interval Probability ◽  
Fokker Planck Equation ◽  
Fokker Planck

The Fokker-Planck equation is widely used to describe the time evolution of stochastic systems in drift-diffusion processes. Yet, it does not differentiate two types of uncertainties: aleatory uncertainty that is inherent randomness and epistemic uncertainty due to lack of perfect knowledge. In this paper, a generalized Fokker-Planck equation based on a new generalized interval probability theory is proposed to describe drift-diffusion processes under both uncertainties, where epistemic uncertainty is modeled by the generalized interval while the aleatory one is by the probability measure. A path integral approach is developed to numerically solve the generalized Fokker-Planck equation. The resulted interval-valued probability density functions rigorously bound the real-valued ones computed from the classical path integral method. The new approach is demonstrated by numerical examples.

Intrinsic Path Integral Solution to the Fokker-Planck Equation

1980 ◽  
pp. 225-248
Author(s):  
Luis Garrido ◽  
Josep Llosa
Keyword(s):  
Path Integral ◽  
Planck Equation ◽  
Integral Solution ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals ON A FRACTIONAL STOCHASTIC PATH INTEGRAL APPROACH IN MODELLING INTERNEURONAL CONNECTIVITY

2012 ◽  
Vol 17 ◽  
pp. 23-33 ◽  
Author(s):  
CHRISTOPHER C. BERNIDO ◽  
M. VICTORIA CARPIO-BERNIDO
Keyword(s):  
Path Integral ◽  
Planck Equation ◽  
Integral Approach ◽  
Strong Correlations ◽  
Path Integral Approach ◽  
Neuronal Communication ◽  
Distant Target ◽  
Short Memory ◽  
Receptor Neurons ◽  
Probability Density Function Pdf

A fractional stochastic path integral approach is presented as a natural framework for treating the random distribution of possible communication chains in the synaptic transmission of signals between initiator and distant target receptor neurons. Fractional Brownian motion parametrization is invoked to account for strong correlations between segments of a neuronal communication chain. We then obtain the probability density function (pdf) for the location of the target receptor neuron in terms of the Hurst index that classifies the dynamics into short-memory or long-memory domains. This pdf obtained by the path integral approach is a fundamental solution of the corresponding Fokker-Planck equation.

Path Integral Associated with the Fokker-Planck Equation

1978 ◽  
pp. 39-60 ◽  
Author(s):  
B. Mühlschlegel
Keyword(s):  
Path Integral ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck
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