The First Attempt on the Stochastic Calculus on Time Scale

DOI10.1080/07362994.2011.610169zbMath1238.60061OpenAlexW1967352105MaRDI QIDQ3114571

Nguyen Thanh Dieu, Nguyen Huu Du

Publication date: 19 February 2012

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362994.2011.610169

zbMATH Keywords

martingalestochastic integrationtime scaleItô's formula\(\nabla\)-stochastic integralDoob-Mayer decompositionLebesgue-Stieltjes \(\nabla\)-integralLebesgue-Stieltjes measure on time scalenatural increasing process

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Martingales with continuous parameter (60G44) Diffusion processes (60J60) Stochastic integrals (60H05) Real analysis on time scales or measure chains (26E70) Stochastic difference equations (39A50)

Related Items (11)

Stochastic dynamic equations on time scales ⋮ Itô's formula, the stochastic exponential, and change of measure on general time scales ⋮ Stochastic linear quadratic control problem on time scales ⋮ Memoryless properties on time scales ⋮ On the stability of stochastic dynamic equations on time scales ⋮ A survey of recent results for the generalizations of ordinary differential equations ⋮ Time scale in least square method ⋮ Dynamic programming and Hamilton-Jacobi-Bellman equations on time scales ⋮ Square mean almost automorphic solution of stochastic evolution equations with impulses on time scales ⋮ Stability of stochastic dynamic equations with time-varying delay on time scales ⋮ Linear feedback of mean-field stochastic linear quadratic optimal control problems on time scales

Cites Work

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• Analysis on measure chains - a unified approach to continuous and discrete calculus
• Expression of the Lebesgue \(\Delta\)-integral on time scales as a usual Lebesgue integral; application to the calculus of \(\Delta\)-antiderivatives
• Brownian motion on disconnected sets, basic hypergeometric functions, and some continued fractions of Ramanujan
• Foundations of Modern Probability
• A DISCRETE-TIME ITÔ'S FORMULA

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