【摘要】 本文通过对随机黎曼和的依测度收敛来定义一种随机积分,并得到使这种积分存在的一些充分条件。更多还原

【Abstract】 We consider the stochastic integral integral from a to b(f(t)dy(t)) where f(t) is a separable, continuous in measure stochastic process ard y(t) satisfies the foUowing conditions: E{|y(t)-y(s)||}≤F(t)-F(s), a.s. E{|y(t)-y(s)|~2|}≤F(t)-F(s), a.s. _t is a family of σ-algebras, _j_t, s<t, s,t[a, b], y(t) is measurable with respect to _t and E(y~2(t))<+∞, F(t) is a monotone non-decreasing function on [a,b]. In defining the integral, we make use of the random Riemann sum. The existence of such integral in the sense of convergence in measure is discussed. The integral above is a generalization of Wiener integral and can be used to handle stochastic integral of higher order.更多还原