Stochastic Differential Equations

Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications. Springer.

Type

Book

Intellectual base

Review or monograph

Year

2003

DOI

10.1007/978-3-642-14394-6

ISBN

9783540047582

DOI registrant

Springer Nature

Link

https://doi.org/10.1007/978-3-642-14394-6

Cited by

7 citations across 6 artifacts.

Domain-specific

• Diffusion Process
  • where \(b\) is the drift, \(W_t\) is Brownian motion, and \(a=\sigma\sigma^{\mathsf T}\) is the local covariance or diffusion matrix.
• Filtering problem (stochastic processes)
  • … recursion, estimate and loss criterion, linear-Gaussian nonlinear and finite-state variants, stability and model-mismatch boundary and distinction from prediction and smoothing are explicit. to An applied instance preserves the invariant under changed notation, scale, dataset, jurisdiction, or implementation..
• Generalized Wiener process
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Geometric Brownian motion
  • Conceptual stochastic-model identity only; financial decisions require current data, model-risk analysis and qualified advice.
• Itô isometry
  • The basic Brownian form extends by completion from simple predictable processes and has variants for martingales and random measures; integrability, filtration and quadratic variation conventions are constitutive.
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Local martingale
  • Localizing sequences, filtration, path regularity and integrability must be declared; strict local martingales need not preserve expectation globally.

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