Abstract
In this paper, we obtain a maximum principle for controlled fractional Fokker-Planck equations. We prove the well-posedness of a stochastic differential equation driven by an α-stable process. We give some estimates of the solutions by fractional calculus. A linear-quadratic example is given at the end of the paper.
Highlights
The real world is full of uncertainty; using stochastic models one may gain real benefits
Stochastic differential equations driven by Brownian motions have been studied extensively
Magdziarz [ ] and Lv et al [ ] obtained the stochastic representation on the fractional Fokker-Planck equation with time and space dependent drift and diffusion coefficients. They found that the corresponding stochastic process is driven by an inverse α-stable subordinator and Brownian motion
Summary
The real world is full of uncertainty; using stochastic models one may gain real benefits. They found that the corresponding stochastic process is driven by an inverse α-stable subordinator and Brownian motion. The fractional Fokker-Planck equation can be described by the following stochastic process (see [ ]): dx(t) = f x(t) dSα(t) + g x(t) dB Sα(t) , with initial value x( ) = ξ . We consider an optimal control problem for fractional Fokker-Planck equations.
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