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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Lluís Quer-Sardanyons, Marta Sanz-Solé (2003)
RACSAM
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We prove existence of density for the real-valued solution to a 3-dimensional stochastic wave equation (...).
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. (2010)
International Journal of Mathematics and Mathematical Sciences
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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.
Balachandran, K., Kim, J.-H. (2006)
Journal of Applied Mathematics and Stochastic Analysis
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Dražen Pantić (1994)
Publications de l'Institut Mathématique
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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...
Samy Tindel (2000)
Applicationes Mathematicae
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We consider the equation du(t,x)=Lu(t,x)+b(u(t,x))dtdx+σ(u(t,x))dW(t,x) where t belongs to a real interval [0,T], x belongs to an open (not necessarily bounded) domain , and L is a pseudodifferential operator. We show that under sufficient smoothness and nondegeneracy conditions on L, the law of the solution u(t,x) at a fixed point is absolutely continuous with respect to the Lebesgue measure.
Saleh, M.M., El-Kalla, I.L., Ehab, M.M. (2007)
Differential Equations & Nonlinear Mechanics
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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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