Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it possible to use the data to find high-probability samples at relatively low cost, making the assimilation more efficient. A new analysis of the feasibility of...
In this paper we extend the results of the research started by the first author in which Karlin-McGregor diagonalization of certain reversible Markov chains over countably infinite general state spaces by orthogonal polynomials was used to estimate the rate of convergence to a stationary distribution. We use a method of...
The convolution inequality h ∗ h(ξ) ≤ B|ξ|θh(ξ) defined on Rⁿ
arises from a probabilistic representation of solutions of the n-dimensional
Navier-Stokes equations, n ≥ 2. Using a chaining argument, we establish
in all dimensions n ≥ 1 the nonexistence of strictly positive fully supported
solutions of this inequality for...