Electronic Journal of Probability · 2011 · 20 citations · 11 references
EngineeringMathematicsProbability TheoryStochastic ModelingStochastic ProcessesBrownian MotionContinuous-time Stochastic ProcessesDiffusion ProcessesMarkov ProcessesStochastic CalculusStochastic Differential EquationsStochastic Flows
We define an equation on a simple graph which is an extension of Tanaka's equation and the skew Brownian motion equation. We then apply the theory of transition kernels developed by Le Jan and Raimond and show that all the solutions can be classified by probability measures.
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J. Michael Harrison, L. A. Shepp · The Annals of Probability · 1981 · 323 citations · Full text
Yves Le Jan, Olivier Raimond · The Annals of Probability · 2004 · 188 citations · Full text
Engineering, Mathematics, Physics +17
On the constructions of the skew Brownian motion
Probability Surveys · 2006 · 178 citations · Full text
On the Constructions of the Skew Brownian Motion
2005 · 156 citations
Integration of Brownian vector fields
Yves Le Jan, Olivier Raimond · The Annals of Probability · 2002 · 139 citations · Full text