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Exponential mixtures of exponentials are Pareto

Did you know that if XE(λ) and L(Y|X=x)=E(x) for all x0 then Y follows a Pareto distribution with  probability density function x1/(λ+x)2? Funny!

Consider now the kinetic diffusion process (Xt,Yt)t0 on R2 where

{dXt=dBts(Xt)λdtdYt=dWts(Yt)|Xt|dt where (Bt)t0 and (Wt)t0 are independent standard Brownian motions and s is the sign function... Can you guess the invariant measure and control the speed of convergence?

2 Comments

  1. Djalil 2010-05-08

    Hello Arthur,

    merci pour ton message et ton lien. Pour Captcha, il y a une petite icône sur le côté de l'image qui permet de générer un code. Il faut appuyer dessus jusqu'à l'obtention de quelque chose de lisible.

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