Summary
In this paper we prove the existence of solutions for a stochastic differential equation inR d, when the drift and the diffusion term are allowed to depend on a specific way on the local time of thedth coordinate of the process to be constructed. The methods of our construction are of purely probabilistic nature.
References
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Takanobu, S. On the existence of solutions of stochastic differential equations with singular drifts. Probab. Th. Rel. Fields 74, 295–315 (1987). https://doi.org/10.1007/BF00569995
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DOI: https://doi.org/10.1007/BF00569995
Keywords
- Differential Equation
- Stochastic Process
- Probability Theory
- Local Time
- Mathematical Biology