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1.
In this paper, we shall firstly illustrate why we should consider integral of a stochastic process with respect to a set-valued square integrable martingale. Secondly, we shall prove the representation theorem of set-valued square integrable martingale. Thirdly, we shall give the definition of stochastic integral of a stochastic process with respect to a set-valued square integrable martingale and the representation theorem of this kind of integrals. Finally, we shall prove that the stochastic integral is a set-valued sub-martingale. 相似文献
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本文定义了一类有界可料过程关于集值平方可积鞅的集值随机积分,并研究了集植随机积分的性质。此为建立集值随机分析的理论奠定了基础。 相似文献
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《随机分析与应用》2013,31(5):1141-1168
Abstract The main aim of this paper is to describe the space of operator‐valued predictable processes, which are integrable with respect to a Hilbert space valued quasi‐left continuous semimartingale. The space of integrable processes is a randomized Musielak‐Orlicz space with a modular explicitely expressed in terms of Jacod‐Grigelionis characteristics. 相似文献
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N.U. Ahmed 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(9-10):3695-3706
In this paper we consider linear filtering for discontinuous processes determined by stochastic differential equations on a Hilbert space driven by signed measures in addition to Brownian motion. The dynamics of the observed data is governed by a differential equation driven by a square integrable martingale (not necessarily continuous) while perturbed by a signed measure. We formulate the filtering problem as an optimization problem on the space of bounded linear operator valued functions and present necessary and sufficient conditions for optimality. Further, we prove, under the assumption of finite dimensionality of the output space, that a Kalman-like filter exists and it is explicitly determined by a Riccati type evolution equation. 相似文献
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Recently, van Neerven, Weis and the author, constructed a theory for stochastic integration of UMD Banach space valued processes. Here the authors use a (cylindrical) Brownian motion as an integrator. In this note we show how one can extend these results to the case where the integrator is an arbitrary real-valued continuous local martingale. We give several characterizations of integrability and prove a version of the Itô isometry, the Burkholder–Davis–Gundy inequality, the Itô formula and the martingale representation theorem. 相似文献
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设X=(Xt,t0)为局部平方可积鞅,且Xo=0,<X,X>t为其二阶可料变差.利用连续半鞅的强逼近结果,我们证明了在较弱的条件下,X的Chung重对数律成立,即 相似文献
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A.U. Kussmaul 《Journal of multivariate analysis》1980,10(1):107-122
A new technique is developed which allows to study quasimartingales with values in a Banach space E via real quasimartingales. As a byproduct path compactness for a wide class of E-valued quasimartingales is proved. The first application of this technique yields the equivalence of a.s. convergence and path compactness for E-valued martingales. Furthermore local decomposability of an E-valued semimartingale into a square integrable martingale and a process of integrable variation is established. Finally, it is shown that each process of integrable variation, with values in a Banach space with Radon-Nikodym property, can be approximated by processes taking values in a finite-dimensional subspace. 相似文献
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Examples of square integrable martingales adapted to processes with independent increments and orthogonal to all stochastic integrals are constructed. If every square integrable martingale adapted to a process with stationary independent increments is a stochastic integral it is shown that the process must be a Wiener process. 相似文献
12.
We prove the Ito formula (1.3) for Banach valued functions acting on stochastic processes with jumps, the martingale part given by stochastic integrals of time dependent Banach valued random functions w.r.t. compensated Poisson random measures. Such stochastic integrals have been discussed by Mandrekar and Rüdiger, Stochastics and Stochastic Reports 78(4), 189–212 (2006) and Rüdiger (2004), Stochastics and Stochastic Reports, 76, pp. 213–242. 相似文献
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T.E Duncan 《Journal of multivariate analysis》1976,6(3):397-413
Stochastic integrals are constructed with values in a compact Riemann manifold from a continuous martingale integrator that is given in the tangent space of the initial point of the stochastic integral and from a stochastic tensor field of linear endomorphisms of the tangent bundle. The integrals that are formed are continuous processes that suitably preserve the martingale property. These stochastic integrals should be useful for the applications of a stochastic calculus in Riemann manifolds. 相似文献
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自反B空间中集值增过程的对偶投影 总被引:8,自引:0,他引:8
假定A是以自反Banach空间中弱紧凸集为值的集值增过程,本文研究了非负有界可测过程关于A的积分以及A在乘积可测空间上生成的集值测度,证明了每个可积集值增过程存在唯一对偶可选(可料)投影. 相似文献
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Wen Chi KUO Coenraad C. A. LABUSCHAGNE Bruce A. WATSON 《数学学报(英文版)》2008,24(2):329-342
The concepts of conditional expectations, martingales and stopping times were extended to the Riesz space context by Kuo, Labuschagne and Watson (Discrete time stochastic processes on Riesz spaces, Indag. Math.,15(2004), 435-451). Here we extend the definition of an asymptotic martingale (amart) to the Riesz spaces context, and prove that Riesz space amarts can be decomposed into the sum of a martingale and an adapted sequence convergent to zero. Consequently an amart convergence theorem is deduced. 相似文献
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Duality theorem for B‐valued martingale Orlicz–Hardy spaces associated with concave functions 下载免费PDF全文
Lin Yu 《Mathematische Nachrichten》2016,289(5-6):756-774
The dual space of B ‐valued martingale Orlicz–Hardy space with a concave function Φ, which is associated with the conditional p‐variation of B ‐valued martingale, is characterized. To obtain the results, a new type of Campanato spaces for B ‐valued martingales is introduced and the classical technique of atomic decompositions is improved. Some results obtained here are connected closely with the p‐uniform smoothness and q‐uniform convexity of the underlying Banach space. 相似文献
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应用原子分解方法,讨论了一类Banach空间值鞅Hardy空间的实内插,推广了Weisz[3]中的相应结论 相似文献
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Fu Qing Gao 《数学学报(英文版)》2009,25(2):209-222
Three types of laws of the iterated logarithm (LIL) for locally square integrable martingales with continuous parameter are considered by a discretization approach. By this approach, a lower bound of LIL and a number of FLIL are obtained, and Chung LIL is extended. 相似文献
19.
A stochastic integral of Banach space valued deterministic functions with respect to Banach space valued Lévy processes is defined. There are no conditions on the Banach spaces or on the Lévy processes. The integral is defined analogously to the Pettis integral. The integrability of a function is characterized by means of a radonifying property of an integral operator associated with the integrand. The integral is used to prove a Lévy–Itô decomposition for Banach space valued Lévy processes and to study existence and uniqueness of solutions of stochastic Cauchy problems driven by Lévy processes. 相似文献
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Shixin Gan 《数学学报(英文版)》1999,15(2):187-196
In this paper, we prove that under theF
4 conditions, anyL log+
L bounded two-parameter Banach spece valued martingale converges almost surely to an integrable Banach space valued random
variable if and only if the Banach space has the Radon-Nikodym property. We further prove that the above conclusion remains
true if theF
4 condition is replaced by the weaker localF
4 condition.
Project supported by the National Natural Science Foundation of China and the State Education Commission Ph. D. Station Foundation 相似文献