An approach to the stochastic calculus in the non-Gaussian case.
Dorogovtsev, Andrej A. (1995)
Journal of Applied Mathematics and Stochastic Analysis
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Dorogovtsev, Andrej A. (1995)
Journal of Applied Mathematics and Stochastic Analysis
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Michał Kisielewicz (1997)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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The definition and some existence theorems for stochastic differential inclusions depending only on selections theorems are given.
Michał Kisielewicz (1999)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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The definition and some existence theorems for stochastic differential inclusion dZₜ ∈ F(Zₜ)dXₜ, where F and X are set valued stochastic processes, are given.
M. Métivier, J. Pellaumail (1976)
Publications mathématiques et informatique de Rennes
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M. Métivier, J. Pellaumail (1977)
Publications mathématiques et informatique de Rennes
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J. Gani (1966-1967)
Publications mathématiques et informatique de Rennes
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T. Barth, A. U. Kussmaul (1981)
Annales scientifiques de l'Université de Clermont. Mathématiques
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Z. Ivković, J. Vukmirović (1976)
Matematički Vesnik
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Tudor, Ciprian A. (2004)
Journal of Applied Mathematics and Stochastic Analysis
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Artstein, Zvi, Wets, Roger J.B. (1995)
Journal of Convex Analysis
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Michał Kisielewicz (2006)
Discussiones Mathematicae Probability and Statistics
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Some sufficient conditins for tightness of continuous stochastic processes is given. It is verified that in the classical tightness sufficient conditions for continuous stochastic processes it is possible to take a continuous nondecreasing stochastic process instead of a deterministic function one.
Sridharan, V., Kalyani, T.V. (2005)
APPS. Applied Sciences
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Fabio Bagarello (2006)
Banach Center Publications
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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...
A. Plucińska (1971)
Applicationes Mathematicae
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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.