Related papers: A stochastic representation theorem for sublinear …
We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…
We present a general derivation of semi-fermionic representation for generators of SU(N) group as a bilinear combination of Fermi operators. The constraints are fulfilled by means of imaginary Lagrange multipliers. The important case of…
In this paper, an approach to estimating a nonlinear deterministic model is presented. We introduce a stochastic model with extremely small variances so that the deterministic and stochastic models are essentially indistinguishable from…
The purpose of this comment is to correct mistaken assumptions and claims made in the paper Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations by T. D. Frank. Our comment centers on the claims…
We introduce a new family of estimators for unnormalized statistical models. Our family of estimators is parameterized by two nonlinear functions and uses a single sample from an auxiliary distribution, generalizing Maximum Likelihood Monte…
We prove the comparison principle for viscosity sub and super solutions of degenerate nonlocal operators with general nonlocal gradient nonlinearities. The proofs apply to purely Hamilton-Jacobi equations of order $0<s<1$.
We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…
A method to construct in explicit form the generators of the simple roots of an arbitrary finite-dimensional representation of a quantum or standard semisimple algebra is found. The method is based on general results from the global theory…
In this paper we present a complete description of a stochastic semigroup of finite-dimensional projections in Hilbert space. The geometry of such semigroups is characterized by the asymptotic behavior of the widths of compact subsets with…
It is known that the stochastic generators of effective processes associated with the unconditioned dynamics of rare events might consist of non-local interactions; however, it can be shown that there are special cases for which these…
We prove global existence, uniqueness and regularity of the mild, Lp and classical solution of a non-linear Fokker-Planck equation arising in an adaptive importance sampling method for molecular dynamics calculations. The non- linear term…
We provide a honesty theory of substochastic evolution families in real abstract state space, extending to an non-autonomous setting the result obtained for $C_0$-semigroups in our recent contribution \textit{[On perturbed substochastic…
In this paper, by using the representation theorem for sublinear expectations, we give a simple proof to obtain two inequalities about the sample mean for independent random vectors under sublinear expectations.
This survey describes the method of approximation of operator semigroups, based on the Chernoff theorem. We outline recent results in this domain as well as clarify relations between constructed approximations, stochastic processes,…
We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…
We consider the setting of either a general non-local branching particle process or a general non-local superprocess, in both cases, with and without immigration. Under the assumption that the mean semigroup has a Perron-Frobenious type…
We connect boundary conditions for one-sided pseudo-differential operators with the generators of modified one-sided L\'evy processes. On one hand this allows modellers to use appropriate boundary conditions with confidence when restricting…
A stochastic representation for the solutions of the Poisson-Vlasov equation is obtained. The representation involves both an exponential and a branching process. The stochastic representation, besides providing an alternative existence…
We study the connections existing between max-infinitely divisible distributions and Poisson processes from the point of view of functional analysis. More precisely, we derive functional identities for the former by using well-known results…
In the recent paper [AF12], we introduced an analysis of the Brylinski-Kostant model for spherical minimal representations for simple real Lie groups of non Hermitian type. We generalize here that analysis and give a unified geometric…