Iterated stochastic measurements

Iterated Stochastic Measurements

We describe a measurement device principle based on discrete iterations of Bayesian updating of system state probability distributions. Although purely classical by nature, these measurements are accompanied with a progressive collapse of the system state probability distribution during each complete system measurement. This measurement scheme finds applications in analysing repeated non-demoli...

An iterated stochastic exemplar model

On the combinatorics of iterated stochastic integrals

Abstract. This paper derives several identities for the iterated integrals of a general semimartingale. They involve powers, brackets, exponential and the stochastic exponential. Their form and derivations are combinatorial. The formulae simplify for continuous or finite-variation semimartingales, especially for counting processes. The results are motivated by chaotic representation of martinga...

Strategies in the Stochastic Iterated Prisoner’s Dilemma

The stochastic iterated prisoner’s dilemma is a kind of iterated prisoner’s dilemma game where the strategies of the players are specified in terms of cooperation probabilities. In particular, if both players use finitememory strategies, then the game can be modeled by a Markov chain. The purpose of this paper is to discuss several important types of strategies related to such a game, especiall...

Series of iterated quantum stochastic integrals

We consider series of iterated non-commutative stochastic integrals of scalar operators on the boson Fock space. We give a sufficient condition for these series to converge and to define a reasonable operator. An application of this criterion gives a condition for the convergence of some formal series of generalized integrator processes such as considered in [CEH]. .