Uniform approximation by random variables

Weak approximation of Heston model by discrete random variables

Least-squares Approximation of Random Variables by Stochastic Integrals∗

This paper addresses the problem of approximating random variables in terms of sums consisting of a real constant and of a stochastic integral with respect to a given semimartingale X. The criterion is minimization of L−distance, or “least-squares”. This problem has a straightforward and well-known solution when X is a Brownian motion or, more generally, a square-integrable martingale, with res...

Weak Approximation of Cir Equation by Discrete Random Variables

For the CIR equation dXt = (θ − kXt) dt + σ √ Xt dBt, we propose positive weak firstand second-order approximations that use, at each step, generation of discrete (respectively twoand three-valued) random variables (Theorems 3 and 4). The equation is split into deterministic part dDt = (θ − kDt) dt, which is solved exactly, and stochastic part dSt = σ √ St dBt, which is actually approximated in...

On the bounds in Poisson approximation for independent geometric distributed random variables

‎The main purpose of this note is to establish some bounds in Poisson approximation for row-wise arrays of independent geometric distributed random variables using the operator method‎. ‎Some results related to random sums of independent geometric distributed random variables are also investigated.

Uniform Approximation by Elementary Operators

On a separable C-algebra A every (completely) bounded map which preserves closed two sided ideals can be approximated uniformly by elementary operators if and only if A is a finite direct sum of C-algebras of continuous sections vanishing at ∞ of locally trivial C-bundles of finite type.