We consider a kind of site-dependent branching Brownian motions whose branching laws depend on the site-branching factor σ（·）. We focus on the functional ergodic limits for the occupation time processes of the...We consider a kind of site-dependent branching Brownian motions whose branching laws depend on the site-branching factor σ（·）. We focus on the functional ergodic limits for the occupation time processes of the models in IR. It is proved that the limiting process has the form of λζ（·）, where A is the Lebesgue measure on R and ζ（·） is a real-valued process which is non-degenerate if and only if cr is integrable. When ζ（·） is non-degenerate, it is strictly positive for t 〉 0. Moreover, ζ converges to 0 in finite-dimensional distributions if the integral of a tends to infinity.展开更多
基金supported by Innovation Program of Shanghai Municipal Education Commission(Grant No.13zz037)the Fundamental Research Funds for the Central Universities
文摘We consider a kind of site-dependent branching Brownian motions whose branching laws depend on the site-branching factor σ（·）. We focus on the functional ergodic limits for the occupation time processes of the models in IR. It is proved that the limiting process has the form of λζ（·）, where A is the Lebesgue measure on R and ζ（·） is a real-valued process which is non-degenerate if and only if cr is integrable. When ζ（·） is non-degenerate, it is strictly positive for t 〉 0. Moreover, ζ converges to 0 in finite-dimensional distributions if the integral of a tends to infinity.
