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Everything about Wiener process
Stochastic process generalizing Brownian motion
In mathematics, the Wiener process is a real-valued continuous-time stochastic process named after Norbert Wiener. It is one of the best known Lévy processes. It occurs frequently in pure and applied mathematics, economics, quantitative finance, evolutionary biology, and physics. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Wiener processA 5-minute orientation
- Skim a recent paper: A multi-phase Wiener process-based degradation model with imperfect maintenance activitiesInfluential work since 2022
- Pick up a classic book: Schrödinger operators, Markov semigroups, wavelet analysis, operator algebrasThe most-reprinted book on the subject
- Read the landmark paper: Sample Functions of the $N$-Parameter Wiener ProcessCited 120 times
- Go sideways: Local martingaleA closely related topic
- Go sideways: Itô calculusA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Sample Functions of the $N$-Parameter Wiener Process
Symbolic Calculus of the Wiener Process and Wiener-Hermite Functionals
On Modeling Bivariate Wiener Degradation Process
A First Passage Problem for the Wiener Process
On the Transformation of the Diffusion Process to a Wiener Process
RUL prediction based on two‐phase wiener process
On Stopping Times for a Wiener Process
Wiener Model Identification of Blast Furnace Ironmaking Process
🆕 Influential since 2022
A multi-phase Wiener process-based degradation model with imperfect maintenance activities
Modeling product degradation with heterogeneity: A general random-effects Wiener process approach
Disturbance-Encoding-Based Neural Hammerstein–Wiener Model for Industrial Process Predictive Control
A Wiener-process-inspired semi-stochastic filtering approach for prognostics
Cutting tool wear prediction based on the multi-stage Wiener process
📚 Books worth reading
Schrödinger operators, Markov semigroups, wavelet analysis, operator algebrasMichael Demuth, Elmar Schrohe · 1996
Stochastic processes and the Wiener integralJui-ching Yeh · 1973
White noise calculus and Fock spaceNobuaki Obata · 1994
White noise distribution theoryHui-Hsiung Kuo · 1996- 📕Complex white noise and infinite dimensional unitary groupTakeyuki Hida · 1971
Multiple Wienerito Integrals
Lecture Notes in MathematicsPeter Major · 2013- 📕Stochastic evolution equations and white noise analysisYoshio Miyahara · 1982
Multiple Wiener-Itô integralsPéter Major · 1981
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Local martingale In mathematics, a local martingale is a type of stochastic process, satisfying the localized version of the martingale property. Every martingale is a…
- Itô calculus Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important…
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- Brownian meander In the mathematical theory of probability, a Brownian meander is a stochastic process that is derived from a standard Brownian motion by conditioning it…
- Girsanov theorem In probability theory, Girsanov's theorem or the Cameron-Martin-Girsanov theorem explains how stochastic processes change under changes in measure. The…
- Lévy process In probability theory, a Lévy process, named after the French mathematician Paul Lévy, is a stochastic process with independent, stationary increments:…
- Tanaka's formula In the stochastic calculus, Tanaka's formula for the Brownian motion states that | B t | = ∫ 0 t sgn ( B s ) d B s + L t {\displaystyle |B_{t}|=\int…
- Local time (mathematics) In the mathematical theory of stochastic processes, local time is a stochastic process associated with semimartingale processes such as Brownian motion…