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On a class of stochastic integrals
Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 1988Let (\(\Omega\),\({\mathcal F},P)\) 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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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 +1 more
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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 +1 more
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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 a Generalization of a Stochastic Integral
Theory of Probability & Its Applications, 1976openaire +2 more sources
1998
AbstractThis chapter discusses the modelling of asset prices as continuous time stochastic processes. Diffusion processes and stochastic differential equations are used as building blocks to obtain the most complete and elegant theory. Practice exercises are included.
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AbstractThis chapter discusses the modelling of asset prices as continuous time stochastic processes. Diffusion processes and stochastic differential equations are used as building blocks to obtain the most complete and elegant theory. Practice exercises are included.
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Stochastic Integrals and Stochastic Functional Equations
SIAM Journal on Applied Mathematics, 1969openaire +1 more source
On an Identity for Stochastic Integrals
Theory of Probability & Its Applications, 1973openaire +1 more source
On a new set-valued stochastic integral with respect to semimartingales and its applications
Journal of Mathematical Analysis and Applications, 2013Marek T Malinowski
exaly
Quantitative approximation of certain stochastic integrals
Stochastic and Stochastics Reports, 2002Stefan Geiss
exaly
A wavelet-based computational method for solving stochastic Itô–Volterra integral equations
Journal of Computational Physics, 2015Fakhrodin Mohammadi
exaly