This paper considers some one dimensional reaction diffusion equations driven by a one dimensional multiplicative white noise. The existence of a stochastic travelling wave solution is established, as well as a sufficient condition to be in its domain of attraction. The arguments use stochastic ordering techniques.

In this paper, we present a new stochastic algorithm, namely the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate the block-coordinate decomposition and an incremental block averaging scheme into the classic (stochastic) mirror-descent method, in order to significantly reduce ...

In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that noisy information about the gradients of the objective function is available via a stochastic first-order oracle (SFO). We propose a general framework for such methods, for which we prove almost sure convergence to stationary points and analyze its worst-case iteration complexity. ...

this paper discusses the problem of allocation of constrained renewable resource to splittable activities of a single project. if the activities of stochastic projects can be split, these projects may be completed in shorter time when the available resource is constrained. it is assumed that the resource amount required to accom-plish each activity is a discrete quantity and deterministic. the ...

representation and modeling of economic uncertainty is addressed by different modeling methods, namely stochastic variables and probabilities, interval analysis, and fuzzy numbers, in particular triple estimates. fo-cusing on discounted cash flow analysis numerical results are presented, comparisons are made between alter-native modeling methods, and characteristics of the methods are discussed.

Runge-Kutta methods are the classic family of solvers for ordinary differential equations (ODEs), and the basis for the state of the art. Like most numerical methods, they return point estimates. We construct a family of probabilistic numerical methods that instead return a Gauss-Markov process defining a probability distribution over the ODE solution. In contrast to prior work, we construct th...

We review a recently devised Monte Carlo simulation method for the direct study of quasi-stationary properties of stochastic processes with an absorbing state. The method is used to determine the static correlation function and the interparticle gap-length distribution in the critical one-dimensional contact process. We also find evidence for power-law decay of the interparticle distance distri...