标题： 关于q-变形量子随机分析 显示英文标题

标题： On q-deformed quantum stochastic calculus

摘要： 在本文中，我们研究了一种由创建、湮灭和粒子数算子构建的量子随机微积分，这些算子满足一些变形的对易关系。 具体来说，我们引入了一种粒子数算子的变形，该算子与已知的q变形创建和湮灭算子具有简单的对易关系。 由于该理论中考虑的所有算子都是有界的，因此我们不涉及Hudson和Parthasarathy非变形理论中的一些困难。 我们定义了随机积分并在算子范数下对其进行了估计。 我们还证明了伊藤公式。 显示英文摘要

摘要： In this paper we investigate a quantum stochastic calculus build of creation, annihilation and number of particles operators which fulfill some deformed commutation relations. Namely, we introduce a deformation of a number of particles operator which has simple commutation relations with well known q-deformed creation and annihilation operators. Since all operators considered in this theory are bounded we do not deal with some difficulties of a non deformed theory of Hudson and Parthasarathy. We define stochastic integrals and estimate them in the operator norm. We prove Ito's formula as well.