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The differential equations of birth-and-death processes, and the Stieltjes moment problem
Transactions of the American Mathematical Society · 1957 · Vol. 85(2) · pp. 489–546
Abstract
Chapter I X Mx, t) = 22 Pu(t)Qi(x) 1=0 or equivalently the vector /(*, 0 = P(t)Q(x).This vector satisfies the equation of(x, t) ---= P'(t)Q(x) = P(l)AQ(x) = -xf(x, t), dt and the initial condition fix, 0) = Q(x).Henceor Mx, t) = e-"Qi(x).Now Pn(t) is thejth Fourier coefficient of/,(x, t) and hence
Stochastic processes and statistical mechanicsTheoretical and Computational PhysicsQuantum chaos and dynamical systemsMathematicsInteger (computer science)PiCombinatoricsMathematical physicsGeometry
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References
Diffusion processes in one dimension
Transactions of the American Mathematical Society · 1954 · 515 citations
The Parabolic Differential Equations and the Associated Semi-Groups of Transformations
Annals of Mathematics · 1952 · 747 citations
An introduction to probability theory and its applications
Journal of the Franklin Institute · 1958 · 29,713 citations
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