We introduce a new Markov chain Monte Carlo (MCMC) sampler for infinite-dimensional inverse problems. Our is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt covariance structure of target distribution. extend this first time function spaces, yielding highly efficient gradient-free MCMC algorithm. Because our does not require gradients or posterior estimat...

We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only finite-dimensional approximation of the measurements is available. For large class satisfying Lipschitz we show that same estimate holds even with finite number measurements. also derive globally convergent algorithm based on Landweber iteration. This theory appli...

In this paper, we investigate infinite interval problems for the fractional evolution equations with Hilfer derivative. By using generalized Ascoli–Arzelà theorem and some new techniques, prove existence of mild solutions when semigroup is compact as well noncompact. addition, an example provided to illustrate results.