Abstract
Let ρ(x, t) denote a family of probability density functions parameterized by time t. We show the existence of a family {τ1 : t > 0} of deterministic nonlinear (chaotic) point transformations whose invariant probability density functions are precisely ρ(x, t). In particular, we are interested in the densities that arise from the diffusions. We derive a partial differential equation whose solution yields the family of chaotic maps whose density functions are precisely those of the diffusion.
Highlights
A DESCRIPTION OF STOCHASTIC SYSTEMS USING CHAOTIC MAPSABRAHAM BOYARSKY AND PAWEŁ GO RA Received 28 August 2003 and in revised form 4 February 2004
In this paper, we establish a method for describing flows of probability density functions by means of discrete-time chaotic maps
We show the existence of a family {τt : t > 0} of deterministic nonlinear point transformations whose invariant probability density functions are precisely ρ(x,t)
Summary
ABRAHAM BOYARSKY AND PAWEŁ GO RA Received 28 August 2003 and in revised form 4 February 2004. Let ρ(x,t) denote a family of probability density functions parameterized by time t. We show the existence of a family {τt : t > 0} of deterministic nonlinear (chaotic) point transformations whose invariant probability density functions are precisely ρ(x,t). We are interested in the densities that arise from the diffusions. We derive a partial differential equation whose solution yields the family of chaotic maps whose density functions are precisely those of the diffusion
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