A247226 Decimal expansion of lambda(2), a constant associated with the asymptotic upper tail of the distribution of the first hitting time T_{2,0} for an Ornstein-Uhlenbeck process across the level 2, starting at 0.

9, 7, 2, 7, 4, 5, 9, 5, 8, 5, 8, 8, 4, 3, 4, 5, 1, 9, 7, 7, 1, 6, 6, 9, 3, 5, 3, 3, 5, 9, 7, 2, 4, 7, 5, 3, 4, 9, 6, 6, 1, 5, 5, 1, 5, 8, 2, 8, 3, 9, 6, 7, 9, 9, 9, 6, 6, 6, 0, 6, 2, 6, 9, 1, 6, 7, 5, 9, 8, 7, 4, 6, 2, 7, 9, 4, 4, 4, 3, 2, 3, 1, 4, 9, 7, 8, 6, 1, 0, 6, 5, 7, 9, 5, 0, 8, 2, 7, 9, 3, 0, 8, 8, 9

Offset

-1,1

Links

Table of n, a(n) for n=-1..102.

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

Cf. A249417, A249418, A249445, A249449, A249451.

Sequence in context: A029688 A155792 A354296 * A197834 A173515 A091558

Adjacent sequences: A247223 A247224 A247225 * A247227 A247228 A247229

Keyword

nonn,cons

Author

Jean-François Alcover, Nov 27 2014

Status

approved