Results 271 to 280 of about 34,146 (315)
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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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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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On a Generalization of a Stochastic Integral
Theory of Probability & Its Applications, 1976openaire +2 more sources
Stochastic Integrals and Stochastic Functional Equations
SIAM Journal on Applied Mathematics, 1969openaire +1 more source
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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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 an Identity for Stochastic Integrals
Theory of Probability & Its Applications, 1973openaire +1 more source
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, 2013Marek T Malinowski
exaly
A wavelet-based computational method for solving stochastic Itô–Volterra integral equations
Journal of Computational Physics, 2015Fakhrodin Mohammadi
exaly
Universal Fuzzy Integral Sliding-Mode Controllers for Stochastic Nonlinear Systems
IEEE Transactions on Cybernetics, 2014Qing Gao, Lu Liu, Gang Feng
exaly