### Introduction to the Theory of the It$\widehat{o}$-type Stochastic Integrals and Stochastic Differential Equations

Svetlana Janković (1998)

Zbornik Radova

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Svetlana Janković (1998)

Zbornik Radova

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Anna Karczewska, Jerzy Zabczyk (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We study regularity of stochastic convolutions solving Volterra equations on ${\mathbb{R}}^{d}$ driven by a spatially homogeneous Wiener process. General results are applied to stochastic parabolic equations with fractional powers of Laplacian.

Peter Jaeger (2016)

Formalized Mathematics

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First we give an implementation in Mizar [2] basic important definitions of stochastic finance, i.e. filtration ([9], pp. 183 and 185), adapted stochastic process ([9], p. 185) and predictable stochastic process ([6], p. 224). Second we give some concrete formalization and verification to real world examples. In article [8] we started to define random variables for a similar presentation to the book [6]. Here we continue this study. Next we define the stochastic process. For further...

Balachandran, K., Kim, J.-H. (2010)

International Journal of Mathematics and Mathematical Sciences

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Joachim Syga (2015)

Discussiones Mathematicae Probability and Statistics

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A random measure associated to a semimartingale is introduced. We use it to investigate properties of several types of stochastic integrals and properties of the solution set of Stratonovich-type stochastic inclusion.

Balachandran, K., Kim, J.-H. (2006)

Journal of Applied Mathematics and Stochastic Analysis

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Saleh, M.M., El-Kalla, I.L., Ehab, M.M. (2007)

Differential Equations & Nonlinear Mechanics

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D. Nualart, M. Sanz (1985)

Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications

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Daniel Ocone, Etienne Pardoux (1989)

Annales de l'I.H.P. Probabilités et statistiques

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El-Borai, Mahmoud M. (1980)

International Journal of Mathematics and Mathematical Sciences

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