Evelyn Buckwar, Christopher T.H. Baker,
"Continuous ?-methods for the stochastic pantograph equation"
, in Electronic Transactions on Numerical Analysis (ETNA), Vol. 11, Kent State University, Department of Mathematics and Computer Science, Kent, Seite(n) 131-151, 2000, ISSN: 1068-9613
Original Titel:
Continuous ?-methods for the stochastic pantograph equation
Sprache des Titels:
Englisch
Original Kurzfassung:
We consider a stochastic version of the pantograph equation:
dX(t) = (aX(t) + bX(qt)) dt + (\sigma_1 + \sigma_2 X(t) + \sigma_3 X(qt))dW(t); X(0) = X0; for t \in [0; T], a given Wiener process W and 0 < q < 1. This is an example of an It?o stochastic delay differential
equation with unbounded memory. We give the necessary analytical theory for existence and uniqueness of a strong solution of the above equation, and of strong approximations to the solution obtained by a continuous extension of the \Theta-Euler scheme (\Theta \in [0; 1]). We establish O(\sqrt{h}) mean-square convergence of approximations obtained using
a bounded mesh of uniform step h, rising in the case of additive noise to O(h). Illustrative numerical examples are provided.
Sprache der Kurzfassung:
Englisch
Journal:
Electronic Transactions on Numerical Analysis (ETNA)
Veröffentlicher:
Kent State University, Department of Mathematics and Computer Science, Kent
Forschungs-