OFFSET
-1,1
LINKS
Steven R. Finch, Ornstein-Uhlenbeck Process, May 15, 2004, p. 7. [Cached copy, with permission of the author]
Eric Weisstein's MathWorld, Parabolic Cylinder Function
Wikipedia, Ornstein-Uhlenbeck process
Wikipedia, Parabolic cylinder function
FORMULA
lambda(a) = lim_{t->infinity} (1/t)*log(P(T_{a,0}>t)).
lambda(a) is the zero of D_{-lambda}(-a) closest to 0, where D_nu(x) is the parabolic cylinder function or Weber function.
EXAMPLE
-0.09727459585884345197716693533597247534966155...
MATHEMATICA
lambda[a_?NumericQ] := x /. FindRoot[ParabolicCylinderD[-x, -a] == 0, {x, 0}, WorkingPrecision -> 104]; RealDigits[lambda[2]] // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Nov 27 2014
STATUS
approved