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Bass","submitted_at":"2024-05-09T23:36:06Z","abstract_excerpt":"Consider the Skorokhod equation in the closed first quadrant: \\[ X_t=x_0+ B_t+\\int_0^t{\\bf v}(X_s)\\, dL_s,\\] where $B_t$ is standard 2-dimensional Brownian motion, $X_t$ takes values in the quadrant for all $t$, and $L_t$ is a process that starts at 0, is non-decreasing and continuous, and increases only at those times when $X_t$ is on the boundary of the quadrant. Suppose ${\\bf v}$ equals $(-a_1,1)$ on the positive $x$ axis, equals $(1,-a_2)$ on the positive $y$ axis, and ${\\bf v}(0)$ points into the closed first quadrant. Let $\\theta_i=\\arctan a_i$, $i=1,2$. 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Bass","submitted_at":"2024-05-09T23:36:06Z","abstract_excerpt":"Consider the Skorokhod equation in the closed first quadrant: \\[ X_t=x_0+ B_t+\\int_0^t{\\bf v}(X_s)\\, dL_s,\\] where $B_t$ is standard 2-dimensional Brownian motion, $X_t$ takes values in the quadrant for all $t$, and $L_t$ is a process that starts at 0, is non-decreasing and continuous, and increases only at those times when $X_t$ is on the boundary of the quadrant. Suppose ${\\bf v}$ equals $(-a_1,1)$ on the positive $x$ axis, equals $(1,-a_2)$ on the positive $y$ axis, and ${\\bf v}(0)$ points into the closed first quadrant. Let $\\theta_i=\\arctan a_i$, $i=1,2$. 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