On existence and an asymptotic behavior of random solutions of a class of stochastic functional-integral equations
Dominik Szynal, Stanisław Wędrychowicz (1987)
Colloquium Mathematicae
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Dominik Szynal, Stanisław Wędrychowicz (1987)
Colloquium Mathematicae
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Balachandran, K., Kim, J.-H. (2006)
Journal of Applied Mathematics and Stochastic Analysis
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Balachandran, K., Kim, J.-H. (2010)
International Journal of Mathematics and Mathematical Sciences
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Xiaoyao Jia, Juanjuan Gao, Xiaoquan Ding (2016)
Open Mathematics
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In this paper, we consider the existence of a pullback attractor for the random dynamical system generated by stochastic two-compartment Gray-Scott equation for a multiplicative noise with the homogeneous Neumann boundary condition on a bounded domain of space dimension n ≤ 3. We first show that the stochastic Gray-Scott equation generates a random dynamical system by transforming this stochastic equation into a random one. We also show that the existence of a random attractor for the...
Łukasz Delong (2012)
Applicationes Mathematicae
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We deal with pricing and hedging for a payment process. We investigate a Black-Scholes financial market with stochastic coefficients and a stream of liabilities with claims occurring at random times, continuously over the duration of the contract and at the terminal time. The random times of the claims are generated by a random measure with a stochastic intensity of jumps. The claims are written on the asset traded in the financial market and on the non-tradeable source of risk driven...
Jan Rosiński, Wojbor A. Woyczyński (1987)
Colloquium Mathematicae
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F. Belzunce (2010)
Boletín de Estadística e Investigación Operativa. BEIO
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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.
Chi-Kwong Li, Wing-Keung Wong (1999)
RAIRO - Operations Research - Recherche Opérationnelle
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Dorogovtsev, Andrej A. (1995)
Journal of Applied Mathematics and Stochastic Analysis
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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...
Katarzyna Jańczak-Borkowska (2011)
Bulletin of the Polish Academy of Sciences. Mathematics
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Generalized reflected backward stochastic differential equations have been considered so far only in the case of a deterministic interval. In this paper the existence and uniqueness of solution for generalized reflected backward stochastic differential equations in a convex domain with random terminal time is studied. Applications to the obstacle problem with Neumann boundary conditions for partial differential equations of elliptic type are given.
Antje Mugler, Hans-Jörg Starkloff (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this article we consider elliptic partial differential equations with random coefficients and/or random forcing terms. In the current treatment of such problems by stochastic Galerkin methods it is standard to assume that the random diffusion coefficient is bounded by positive deterministic constants or modeled as lognormal random field. In contrast, we make the significantly weaker assumption that the non-negative random coefficients can be bounded strictly away from zero and infinity...