Infinite dimensional continuous local martingale s

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Infinite dimensional continuous local martingale stochastic integral

. ,, Shape, may be regarded as the space on the Extension of the continuous local martingale, and f [,] = 0 (, k a 1,2, ...), 1 [,]=£( j:, k-1, 2, ....) Today: ft () ai / z (s) ≠ 0jdrY: + J0Σlt v v 』(a v ≠ 0】 d milk (j; = l'2 '...),I (s) (s) n-1 (5), ≠ o} ds a 2I () · JoJo (5) n-1 (5) I) ≠ o} ds = £ (, k a 1,2, ... .) Lemma 2,[link widoczny dla zalogowanych], {. J-l, 2, ...) is infinite independent Brown campaign. note [vii d], = 0} ds-o; [0} d] a nIn (5) I { () 0} ds = 0, then there is a n v ∽ ≠ 0jdWl +.) d Gou a ΣΣl (s) (s) n () v = ≠ 0】 d Gou, Mexico 1 University (Natural Science) Volume 34. 『'. (Sd + good. 『'(S) d00-I port. (S),) ≠. } D + ΣI (s) a JzJ a clam 0} dp-v owl, one I port () J {(,) 一 0} d Xiao A + Σl-tffJ () d =. Theorem is proved. Theorem 1 and by the standard method, the following two inferences can be proved that the process slightly. Corollary 1 equation (1) the existence of weak solutions is equivalent to: there exists a probability space to meet the normal conditions (n, F, F, P) and its continuous adaptation process x, so that for all f ∈ ci (R ), f (X) a, (z) a I (Lf) (x) ds is a continuous local martingale, where L = bd / dx + (1 / 2) (ad. / dx), a = llll. Corollary 2 Let equation (1) the coefficient b ,={,= 1,2, ...} continuous, and satisfy the linear growth condition, that there exists a constant K> O, Vz ∈ R, with II (z) II + I6 ( z) I. ≤ K (1 + II), then the equation (1) The existence of weak solutions. The authors thank Professor Ren Jiagang and Zhang Xicheng encouragement and help. {-} BIBLIOGRAP EliAirauhH, RenJ. Modulusofcontinuityoftheca-nonicbrownianmotion JFunctAnal, 2002,196 (2) :395-426. [23CaoGuilan, HeKai, Onatypeofstochasticdifferen-tialequationsdrivenbycountablymanybrownianmo-tionsl-J]. JFunctAnal, 2003,203 (1) :262-285. [3] Huang Zhiyuan. Fundamentals of stochastic analysis [M]. 2. Beijing; Science Press, 2001. [43RenJ, ZhangX. StochasticflowsforSDEswithnon-lipschitzcoefficients [J]. BullSciMath ,2003,127:739-754. Environment Autoclaved brick has not been very good resources and technology, stacked not only pollute the environment, but also take up land needed maintenance costs, resource utilization as a result of technical problems. Huazhong University of Science and Technology Preparation of unburned brick by Foundry Sand is the main activity use hydrated silicon dioxide and calcium oxide to form calcium silicate hydrate formed by the reaction strength of the principles of the old foundry sand is mainly from the role of aggregates and skeleton will not only consume a large amount of casting sand, sand piled up the old account for effective mitigation to, environmental problems, will the change waste into treasure, made products for sale, can generate a decent profit, is a substantial use of energy resources used sand casting technology, has significant social, environmental wide application. The project technology is the leading domestic level.