From discrete to continuous time

DOI10.1016/0168-0072(91)90042-KzbMath0756.60036MaRDI QIDQ1177039

H. Jerome Keisler

Publication date: 25 June 1992

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

zbMATH Keywords

martingalesstochastic processesforcingnonstandard analysiscontinuous time processesdiscrete time processes

Mathematics Subject Classification ID

Foundations of classical theories (including reverse mathematics) (03B30) Nonstandard models in mathematics (03H05) Axioms; other general questions in probability (60A05) Foundations of stochastic processes (60G05) Nonstandard analysis (26E35)

Cites Work

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• Foundations of infinitesimal stochastic analysis
• Tightness criteria for laws of semimartingales
• Elementary embeddings and games in adapted probability logic
• Construction of a martingale with given absolute value
• A non-standard representation for Brownian motion and Ito integration
• Every nonnegative submartingale is the absolute value of a martingale
• An infinitesimal approach to stochastic analysis
• Nonstandard Construction of the Stochastic Integral and Applications to Stochastic Differential Equations.I
• Adapted Probability Distributions
• Descriptive set theory over hyperfinite sets
• Existence of weak solutions for stochastic differential equations with driving semimartingales
• One Dimensional Stochastic Differential Equations with No Strong Solution
• Star-Finite Representations of Measure Spaces
• Conversion from Nonstandard to Standard Measure Spaces and Applications in Probability Theory
• Analytic Sets, Baire Sets and the Standard Part Map
• Weak Limits of Measures and the Standard Part Map
• Unbounded Loeb Measures
• On the Construction and Distribution of a Local Martingale with a Given Absolute Value
• Non-standard analysis

Related Items (7)

Quantifier elimination for neocompact sets ⋮ Rich and saturated adapted spaces ⋮ On the maximality of logics with approximations ⋮ Neocompact sets and the fixed point property ⋮ On the relation between elementary partial difference equations and partial differential equations ⋮ Non-cooperative games on hyperfinite Loeb spaces ⋮ Continuous vs. discrete time: some computational insights

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