Let X(t) be a diffusion process satisfying the stochastic differential equation dX(t) = a(X(t))dW(t) + b(X(t))dt. We analyse the asymptotic behaviour of p(t) = Prob{X(t) ≥ 0} as t → ∞ and construct an equation such that $lim sup_{t→∞} t^{-1} ∫_0^t p(s) ds = 1$ and $lim inf_{t→∞}t^{-1} ∫_0^t p(s) ds = 0$.
Institute of Mathematics, Polish Academy of Sciences, Staromiejska 8/6, 40-013 Katowice, Poland
Bibliografia
[1] I. I. Gihman and A. V. Skorohod, Stochastic Differential Equations, Springer, Berlin 1972.
[2] A. K. Gushchin and V. P. Mikhailov, The stabilization of the solution of the Cauchy problem for a parabolic equation with one space variable, Trudy Mat. Inst. Steklov. 112 (1971), 181-202 (in Russian).
[3] T. Komorowski and J. Tyrcha, Asymptotic properties of some Markov operators, Bull. Polish Acad. Sci. Math. 37 (1989), 221-228.
[4] R. Rudnicki, Asymptotical stability in L¹ of parabolic equations, J. Differential Equations, in press.
[5] Z. Schuss, Theory and Applications of Stochastic Differential Equations, Wiley, New York 1980.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv58z1p37bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.