On Stochastic Differential Equations |
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B-measurable function B-measurable mapping belongs to d-class Borel field Borel set Borel subset bounded function brownian motion called completely additive class continuous convolution d-class with P-measure denote du/u² DX(t easily verified elementary set existence and uniqueness f F(I F₁(L finite Fokker-Plank equation function of x(w Gaussian distribution homogeneous differential process I₁ implies independent infinitely divisible law J. L. Doob Lemma Lévy limit in probability logarithmic characteristic function Math n(du probability distribution probability field random variable recursively regular kernel S(I₁ satisfies 11.7 satisfies G.3 sequence Similarly simple Markoff process solution of 11.7 Stap stochastic differential equation stochastic integral equation stochastic process t,x t,w temporally homogeneous differential Theorem 11 Theorem 2.2 three elements totally bounded transition probability law uniformly convergent uniformly stepwise function Wiener's