Brownian motion with general drift

D. Kinzebulatov and Yu. A. Semënov

Stochastic Processes and their Applications, 2020, vol. 130, issue 5, 2737-2750

Abstract: We construct and study the weak solution to stochastic differential equation dX(t)=−b(X(t))dt+2dW(t), X(0)=x, for every x∈Rd, d≥3, with b in the class of weakly form-bounded vector fields, containing, as proper subclasses, a sub-critical class [Ld+L∞]d, as well as critical classes such as weak Ld class, Kato class, Campanato–Morrey class.

Keywords: Elliptic operators; Feller processes; Stochastic differential equations (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2019.08.003

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