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- Tanaka_equation abstract "In mathematics, Tanaka's equation is an example of a stochastic differential equation which admits a weak solution but has no strong solution. It is named after the Japanese mathematician Hiroshi Tanaka.Tanaka's equation is the one-dimensional stochastic differential equationdriven by canonical Brownian motion B, with initial condition X0 = 0, where sgn denotes the sign function(Note the unconventional value for sgn(0).) The signum function does not satisfy the Lipschitz continuity condition required for the usual theorems guaranteeing existence and uniqueness of strong solutions. In fact, the Tanaka equation has no strong solution, i.e. one for which the version B of Brownian motion is given in advance and the solution X is adapted to the filtration generated by B and the initial conditions. However, the Tanaka equation does have a weak solution, one for which the process X and version of Brownian motion are both specified as part of the solution, rather than the Brownian motion being given a priori. In this case, simply choose X to be any Brownian motion and define byi.e.Hence,and so X is a weak solution of the Tanaka equation. Furthermore, this solution is weakly unique, i.e. any other weak solution must have the same law.".
- Tanaka_equation wikiPageID "12139471".
- Tanaka_equation wikiPageRevisionID "493502710".
- Tanaka_equation hasPhotoCollection Tanaka_equation.
- Tanaka_equation subject Category:Equations.
- Tanaka_equation subject Category:Stochastic_differential_equations.
- Tanaka_equation type Abstraction100002137.
- Tanaka_equation type Communication100033020.
- Tanaka_equation type DifferentialEquation106670521.
- Tanaka_equation type Equation106669864.
- Tanaka_equation type Equations.
- Tanaka_equation type MathematicalStatement106732169.
- Tanaka_equation type Message106598915.
- Tanaka_equation type Statement106722453.
- Tanaka_equation type StochasticDifferentialEquations.
- Tanaka_equation comment "In mathematics, Tanaka's equation is an example of a stochastic differential equation which admits a weak solution but has no strong solution.".
- Tanaka_equation label "Tanaka equation".
- Tanaka_equation sameAs m.02vr3wp.
- Tanaka_equation sameAs Q7682254.
- Tanaka_equation sameAs Q7682254.
- Tanaka_equation sameAs Tanaka_equation.
- Tanaka_equation wasDerivedFrom Tanaka_equation?oldid=493502710.
- Tanaka_equation isPrimaryTopicOf Tanaka_equation.