Advances in Probability and Related Topics, Volume 3Peter Ney |
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Page 4
... process X , a general prescription for finding all of its MOFs . This leads into explicit operator products in the case of Markov chains and leads into stochastic integral equations in the case of diffusion processes . Our point of view ...
... process X , a general prescription for finding all of its MOFs . This leads into explicit operator products in the case of Markov chains and leads into stochastic integral equations in the case of diffusion processes . Our point of view ...
Page 102
... stochastic processes by weaker " obliqueness " requirements . We now integrate one stochastic process with respect to another . The classical definition in Doob [ 1 ] requires of one of the processes more than orthogonality of ...
... stochastic processes by weaker " obliqueness " requirements . We now integrate one stochastic process with respect to another . The classical definition in Doob [ 1 ] requires of one of the processes more than orthogonality of ...
Page 105
... stochastic processes , so that the word " stochastic " has come to mean the very antithesis of deterministic , instead of its generali- zation . This is illustrated by the fact that the class of functions x ( t , w ) that constitute a ...
... stochastic processes , so that the word " stochastic " has come to mean the very antithesis of deterministic , instead of its generali- zation . This is illustrated by the fact that the class of functions x ( t , w ) that constitute a ...
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argument bounded Brownian motion completes the proof condition constant Corollary corresponding countable defined denote derivative distribution equals equation Example exists follows formula given h-meas Hausdorff Hausdorff measure Hence hypothesis increasing process independent increments inequality Itô Laplace Lemma Lévy measure Lévy process lim inf lim sup limit theorem linear equivalence log log Markov chain Markov process martingale Math multiple points multiplicative operator functional nigh-martingale nonnegative obtain point process Poisson process probability measure proof of Theorem Proposition prove random evolutions random measures random variables result right continuous S₂ sample functions satisfies Section semigroup sequence space stochastic integral stochastic process strictly stable process strongly continuous subordinator T₁ T₂ term Theorem 4.1 theory topology v(dx v(dy values vector Verw Wahr Wiener process write zero αβ