论文标题
反映广义抛物线域中的布朗运动：爆炸和超级抗衰老
Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity
论文作者
论文摘要
对于多维漂移的无漂移扩散，在无界，光滑的，亚线性的广义抛物面结构域中，并具有从边界的倾斜反射，我们给出了自然条件，如果该域在无穷大的范围内足够快地狭窄，否则会发生爆炸，否则我们有超延伸性瞬时，我们可以使用大量的大量法律来量化。例如，在平面域的情况下，且仅当域的面积是有限的时，就会发生爆炸。我们开发并应用新颖的半明天标准来研究爆炸并建立具有独立利益的强大法律。
For a multidimensional driftless diffusion in an unbounded, smooth, sub-linear generalized parabolic domain, with oblique reflection from the boundary, we give natural conditions under which either explosion occurs, if the domain narrows sufficiently fast at infinity, or else there is superdiffusive transience, which we quantify with a strong law of large numbers. For example, in the case of a planar domain, explosion occurs if and only if the area of the domain is finite. We develop and apply novel semimartingale criteria for studying explosions and establishing strong laws, which are of independent interest.
