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This subtopic introduces the core ideas in stochastic analysis, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.
Stochastic integrals. This topic covers stochastic analysis, including stochastic calculus, stochastic differential equations, and analytic tools for random systems.
Wikipedia: Stochastic calculus
Used to analyze continuous-time random dynamics and develop rigorous stochastic PDE/SDE methods.
Stochastic calculus of variations and the Malliavin calculus. This topic covers stochastic analysis, including stochastic calculus, stochastic differential equations, and analytic tools for random systems.
Wikipedia: Stochastic calculus
Used to analyze continuous-time random dynamics and develop rigorous stochastic PDE/SDE methods.
Stochastic ordinary differential equations. This topic covers stochastic analysis, including stochastic calculus, stochastic differential equations, and analytic tools for random systems.
Wikipedia: Stochastic calculus
Used to analyze continuous-time random dynamics and develop rigorous stochastic PDE/SDE methods.
Stochastic partial differential equations. This topic covers stochastic analysis, including stochastic calculus, stochastic differential equations, and analytic tools for random systems.
Wikipedia: Stochastic calculus
Used to analyze continuous-time random dynamics and develop rigorous stochastic PDE/SDE methods.
Stochastic integral equations. This topic covers stochastic analysis, including stochastic calculus, stochastic differential equations, and analytic tools for random systems.
Wikipedia: Stochastic calculus
Used to analyze continuous-time random dynamics and develop rigorous stochastic PDE/SDE methods.
Random operators and equations. This topic covers stochastic analysis, including stochastic calculus, stochastic differential equations, and analytic tools for random systems.
Wikipedia: Stochastic calculus
Used to analyze continuous-time random dynamics and develop rigorous stochastic PDE/SDE methods.
Applications of stochastic analysis. This topic covers stochastic analysis, including stochastic calculus, stochastic differential equations, and analytic tools for random systems.
Wikipedia: Stochastic calculus
Used to analyze continuous-time random dynamics and develop rigorous stochastic PDE/SDE methods.
Computational methods for stochastic equations. This topic covers stochastic analysis, including stochastic calculus, stochastic differential equations, and analytic tools for random systems.
Wikipedia: Stochastic calculus
Used to analyze continuous-time random dynamics and develop rigorous stochastic PDE/SDE methods.
White noise theory. This topic covers stochastic analysis, including stochastic calculus, stochastic differential equations, and analytic tools for random systems.
Wikipedia: Stochastic calculus
Used to analyze continuous-time random dynamics and develop rigorous stochastic PDE/SDE methods.
None of the above. This topic covers stochastic analysis, including stochastic calculus, stochastic differential equations, and analytic tools for random systems.
Wikipedia: Stochastic calculus
Used to analyze continuous-time random dynamics and develop rigorous stochastic PDE/SDE methods.