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Principle Seminar of the Department of Probability Theory, Moscow State University
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Максимальное неравенство для косого броуновского движения M. V. Zhitlukhin |
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Abstract: M. Zhitlukhin MAXIMAL INEQUALITY FOR SKEW BROWNIAN MOTION Let This inequality can be viewed as a generalization of the known inequalities for a standard Brownian motion and its modulus. A. Muravlev On some properties of the local time Let $$ \mathcal{G}u = \alpha u, $$ where $$ \fw(x) = \fpsi'(x) \fphi(x) - \fpsi(x) \fphi'(x), \quad \frho(x,y)=\fpsi(x) \fphi(y) - \fpsi(y) \fphi(x). $$ Let us consider the local time of the diffusion $$ \tau_{ab} = \inf \{ t \ge 0: X_t \not\in (a,b) \}.\\ $$ \begin{theorem} For </nomathmode><mathmode> $$ \Eb_x e^{-\alpha \tau_{ab} - \beta L(\tau_{ab},x)} = \frac{\frho(a,x) + \frho(x,b)}{\frho(a,b) - \frac{2\beta}{\fw(x)} \frho(a,x) \frho(x,b)}. $$ \end{theorem} </mathmode><nomathmode> |