Zeroth-order (derivative-free) optimization attracts a lot of attention in machine learning, because explicit gradient calculations may be computationally expensive or infeasible. To handle large scale problems both in volume and dimension, recently asynchronous doubly stochastic zeroth-order algorithms were proposed. The convergence rate of existing asynchronous doubly stochastic zeroth order ...

It is proved that every doubly stochastic quantum channel that is properly averaged with the completely depolarizing channel can be written as a convex combination of unitary channels. As a consequence, we find that the collection of channels expressible as convex combinations of unitary channels has non-zero Borel measure within the space of doubly stochastic channels.

In this paper, we consider the problem of mean-variance hedging in an incomplete market where the underlying assets are jump diffusion processes which are driven by Brownian motion and doubly stochastic Poisson processes. This problem is formulated as a stochastic control problem and closed form expressions for the optimal hedging policy are obtained using methods from stochastic control and th...

Doubly stochastic measures can be identi ed with the trace of a pair of (Lebesgue) measure preserving maps of the unit interval to itself. It has been of traditional interest in probability theory to produce a random vector (or metric space element), which has a given distribution and is de ned on a standard space, such as [0; 1] endowed with Lebesgue measure. In a classic work, L evy [4, secti...

We consider the class of doubly diagonally dominant matrices (A = [ ajj] E C”, ‘, la,,1 l”jjl > Ck+ i laiklCk+ jlajkl. i #j) and its subclasses. We give necessary and sufficient conditions in terms of the directed graph for an irreducibly doubly diagonally dominant matrix to be a singular matrix or to be an H-matrix. As in the case of diagonal dominance, we show that the Schur complements of do...

The text deals with the problem of detecting anomalies on a background of multi-dimensional images. We synthesized a detection algorithm based on the use of doubly stochastic models of random fields and which requires pre-filtering the image. We propose to use the modified Kalman filter. We also investigated an efficiency of extended signals detection on real images. It is shown that the result...

We prove a general theorem that the L2ρ(R ;R) ⊗ L2ρ(R ;R) valued solution of an infinite horizon backward doubly stochastic differential equation, if exists, gives the stationary solution of the corresponding stochastic partial differential equation. We prove the existence and uniqueness of the L2ρ(R ;R)⊗Lρ(R ;R) valued solutions for backward doubly stochastic differential equations on finite a...

This paper is intended to give a probabilistic representation for stochastic viscosity solution of semi-linear reflected stochastic partial differential equations with nonlinear Neumann boundary condition. We use its connection with reflected generalized backward doubly stochastic differential equations. AMS Subject Classification: 60H15; 60H20

In this paper we study the solvability of backward doubly stochastic differential equations (BDSDEs for short) with polynomial growth coefficients and their connections with SPDEs. The corresponding SPDE is in a very general form, which may depend on the derivative of the solution. We use Wiener-Sobolev compactness arguments to derive a strongly convergent subsequence of approximating SPDEs. Fo...

Two sequential camera source identification methods are proposed. Sequential tests implement a log-likelihood ratio test in an incremental way, thus enabling a reliable decision with a minimal number of observations. One of our methods adapts Goljan et al.’s to sequential operation. The second, which offers better performance in terms of error probabilities and average number of test observatio...