Add to ORKGWe propose two novel unbiased estimators of the integral $\int_{[0,1]^{s}}f(u) du$ for a function $f$, which depend on a smoothness parameter $r\in\mathbb{N}$. The first estimator integrates exactly the polynomials of degrees $p<r$ and achieves the optimal error $n^{-1/2-r/s}$ (where $n$ is the number of evaluations of $f$) when $f$ is $r$ times continuously differentiable. The second estimator is computationally cheaper but it is restricted to functions that vanish on the boundary of $[0,1]^s$. The construction of the two estimators relies on a combination of cubic stratification and control ariates based on numerical derivatives. We provide numerical evidence that they show good performance even for moderate values of $n$
The problem of predicting integrals of stochastic processes is considered. Linear estimators have b...
AbstractGiven an increasing function H:[0,1)→[0,∞) and An(H)≔infτ∈Tn(∑i=1n∫ti−1ti(ti−t)H(t)2dt)12, w...
The problem of predicting integrals of stochastic processes is considered. Linear estimators have b...
We propose two novel unbiased estimators of the integral $\int_{[0,1]^{s}}f(u) du$ for a function $f...
We propose two novel unbiased estimators of the integral $\int_{[0,1]^{s}}f(u) du$ for a function $f...
International audienceWe propose two novel unbiased estimators of the integral $\int_{[0,1]^{s}}f(u)...
AbstractWe show that for functions f∈Lp([0,1]d), where 1≤p≤∞, the family of integrals ∫[0,x]f(t)dt(x...
International audienceWe analyze a Monte Carlo method using stratified sampling for approximate inte...
International audienceWe analyze a Monte Carlo method using stratified sampling for approximate inte...
AbstractDetails are given for a Fortran implementation of an algorithm that uses stochastic spherica...
AbstractWe study the multivariate integration problem ∫Rdf(x)ρ(x)dx, with ρ being a product of univa...
We approximate the integral of a smooth function on [0,1], where values are only known at n random p...
We approximate the integral of a smooth function on [0,1], where values are only known at n random p...
We approximate the integral of a smooth function on [0,1], where values are only known at n random p...
We approximate the integral of a smooth function on [0,1], where values are only known at n random p...
The problem of predicting integrals of stochastic processes is considered. Linear estimators have b...
AbstractGiven an increasing function H:[0,1)→[0,∞) and An(H)≔infτ∈Tn(∑i=1n∫ti−1ti(ti−t)H(t)2dt)12, w...
The problem of predicting integrals of stochastic processes is considered. Linear estimators have b...
We propose two novel unbiased estimators of the integral $\int_{[0,1]^{s}}f(u) du$ for a function $f...
We propose two novel unbiased estimators of the integral $\int_{[0,1]^{s}}f(u) du$ for a function $f...
International audienceWe propose two novel unbiased estimators of the integral $\int_{[0,1]^{s}}f(u)...
AbstractWe show that for functions f∈Lp([0,1]d), where 1≤p≤∞, the family of integrals ∫[0,x]f(t)dt(x...
International audienceWe analyze a Monte Carlo method using stratified sampling for approximate inte...
International audienceWe analyze a Monte Carlo method using stratified sampling for approximate inte...
AbstractDetails are given for a Fortran implementation of an algorithm that uses stochastic spherica...
AbstractWe study the multivariate integration problem ∫Rdf(x)ρ(x)dx, with ρ being a product of univa...
We approximate the integral of a smooth function on [0,1], where values are only known at n random p...
We approximate the integral of a smooth function on [0,1], where values are only known at n random p...
We approximate the integral of a smooth function on [0,1], where values are only known at n random p...
We approximate the integral of a smooth function on [0,1], where values are only known at n random p...
The problem of predicting integrals of stochastic processes is considered. Linear estimators have b...
AbstractGiven an increasing function H:[0,1)→[0,∞) and An(H)≔infτ∈Tn(∑i=1n∫ti−1ti(ti−t)H(t)2dt)12, w...
The problem of predicting integrals of stochastic processes is considered. Linear estimators have b...