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Local time
About: Local time is a research topic. Over the lifetime, 1341 publications have been published within this topic receiving 46986 citations.
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20 Dec 1990TL;DR: In this article, a representation of stochastic processes and response statistics are represented by finite element method and response representation, respectively, and numerical examples are provided for each of them.
Abstract: Representation of stochastic processes stochastic finite element method - response representation stochastic finite element method - response statistics numerical examples.
5,495 citations
TL;DR: Using only the Boson canonical commutation relations and the Riemann-Lebesgue integral, this article constructed a simple theory of stochastic integrals and differentials with respect to the basic field operator processes.
Abstract: Using only the Boson canonical commutation relations and the Riemann-Lebesgue integral we construct a simple theory of stochastic integrals and differentials with respect to the basic field operator processes. This leads to a noncommutative Ito product formula, a realisation of the classical Poisson process in Fock space which gives a noncommutative central limit theorem, the construction of solutions of certain noncommutative stochastic differential equations, and finally to the integration of certain irreversible equations of motion governed by semigroups of completely positive maps. The classical Ito product formula for stochastic differentials with respect to Brownian motion and the Poisson process is a special case.
1,298 citations
1,069 citations