Strangely sweeping one-dimensional diffusion

• Autorzy: Ryszard Rudnicki
• Języki publikacji: EN

Abstrakty

EN

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 $lim inf_{t→∞}t^{-1} ∫_0^t p(s) ds = 0$.

Słowa kluczowe

EN

diffusion process   parabolic equation  

Kategorie tematyczne

• 35K15: Initial value problems for second-order parabolic equations
• 60J60: Diffusion processes

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1993
• Tom: 58
• Numer: 1
• Strony: 37-45

Daty

wydano

1993

otrzymano

1991-10-21

poprawiono

1992-03-04

poprawiono

1992-05-05

Twórcy

autor

Ryszard Rudnicki

• 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.