Results 221 to 230 of about 26,100 (268)

On a class of stochastic integrals

Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 1988
Let (\(\Omega\),\({\mathcal F},P)\) be a probability space. If a random variable X is from \(L^ r(dP)\), \(r>0\), then \(\| X\|_ r=(E| X|^ r)^{1/r}\). The notion of an \(S_{r,p}\) system \((r,p>0)\) was introduced by \textit{F. Moricz} [Acta Sci. Math. 38, 127-144 (1976; Zbl 0325.42007)] in the following way: A sequence \(\{X_ 1,X_ 2,...\}\) of random ...
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Stochastic Integrals and Differential Measures

Theory of Probability & Its Applications, 1988
The description of the class of measures with square integrable logarithmic derivative along a vector field and an operator field is obtained. This derivative coincides with an extended stochastic integral in the Gaussian case. The proofs are based on integration by parts.
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The Stochastic Integral

1990
In this chapter, we define (stochastic) Ito-integrals \(\int_0^t {HdM} \) H dM for local L 2 — martingales M and a fairly large class of adapted processes H. The integral is a random variable. It will be constructed as a suitable limit of Riemann-Stieltjes type approximations like $$\sum\limits_{i = 1}^n {{H_{{s_i}}} \cdot \left( {{M_{s{}_{i + 1}}}
Heinrich von Weizsäcker, Gerhard Winkler   +1 more
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The Stochastic Integral

2015
We have now established enough basic theory to construct the stochastic integral in full generality. In this chapter, we develop the integral with respect to semimartingales, and prove some of its properties. As in the previous chapters, we assume we have a filtered probability space, with filtration satisfying the usual conditions, \(\mathcal{F}_ ...
Samuel N. Cohen, Robert J. Elliott
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The Stochastic Integral

2017
Let \(B = (\varOmega,\mathcal{F},(\mathcal{F}_{t})_{t},(B_{t})_{t},\mathrm{P})\) be a (continuous) standard Brownian motion fixed once and for all: the aim of this chapter is to give a meaning to expressions of the form \(\displaystyle{ \int _{0}^{T}X_{ s}(\omega )\,dB_{s}(\omega ) }\) where the integrand (X s )0 ≤ s ≤ T is a process enjoying certain ...
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On a Generalization of a Stochastic Integral

Theory of Probability & Its Applications, 1976
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Stochastic Integrals and Stochastic Functional Equations

SIAM Journal on Applied Mathematics, 1969
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On an Identity for Stochastic Integrals

Theory of Probability & Its Applications, 1973
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Stochastic Integrals

Abstract This chapter has five sections and is concerned with the distribution of the ‘mean deviation’ components of the covariance described in Chapter 4. Section 1 shows how these terms can be rearranged in a useful manner, as the sums of products of an independent process and a moving average process whose weights are particular ...
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On a new set-valued stochastic integral with respect to semimartingales and its applications

Journal of Mathematical Analysis and Applications, 2013
Marek T Malinowski
exaly