Hallo,

I've to find a constant $\displaystyle C \in \mathbb{R}_+$ such that $\displaystyle |Y_n|\leq C$ for a random variable $\displaystyle Y_n$ which is defined by

$\displaystyle Y_n:=\frac{2 \cdot (\pi e^{\theta (\mu_n h+ \sigma (W_{nh}-W_{(n-1)h})})^3}{(1+\pi( e^{\theta (\mu_n h+ \sigma (W_{nh}-W_{(n-1)h}))}-1))^3}-\frac{ (\pi e^{\theta (\mu_n h+ \sigma (W_{nh}-W_{(n-1)h})})^2}{(1+\pi( e^{\theta (\mu_n h+ \sigma (W_{nh}-W_{(n-1)h}))}-1))^2}$

whereas

$\displaystyle W$ is a standard Brownian motion

$\displaystyle \mu$ is a normal distributed random variable

$\displaystyle \pi$ and $\displaystyle \theta$ are random variables with values in the interval $\displaystyle [0,1]$

$\displaystyle 0<h<1$ is a parameter

$\displaystyle \sigma>0$ is a constant

Can anybody help me finding $\displaystyle C$ such that $\displaystyle |Y_n|\leq C$?

Thanks a lot!!