The Experts below are selected from a list of 57033 Experts worldwide ranked by ideXlab platform
Bernt Oksendal - One of the best experts on this subject based on the ideXlab platform.
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Stochastic Differential Equations - Stochastic Differential Equations
The Mathematical Gazette, 2020Co-Authors: Bernt OksendalAbstract:We now return to the possible solutions X t (ω) of the Stochastic Differential equation (5.1) where W t is 1-dimensional “white noise”. As discussed in Chapter III the Ito interpretation of (5.1) is that X t satisfies the Stochastic integral equation or in Differential form (5.2) .
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Stochastic Differential Games
Applied Stochastic Control of Jump Diffusions, 2019Co-Authors: Bernt Oksendal, Agnès SulemAbstract:In this section we present the dynamic programming approach to Stochastic Differential games. We only present the case for zero sum games. For the extension to non-zero sum games, we refer to [MO].
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Risk minimizing portfolios and HJBI equations for Stochastic Differential games
Stochastics, 2008Co-Authors: Sure Mataramvura, Bernt OksendalAbstract:In this paper, we consider the problem to find a market portfolio that minimizes the convex risk measure of the terminal wealth in a jump diffusion market. We formulate the problem as a two player (zero-sum) Stochastic Differential game. To help us find a solution, we prove a theorem giving the Hamilton-Jacobi-Bellman-Isaacs (HJBI) conditions for a general zero-sum Stochastic Differential game in a jump diffusion setting. We then use the theorem to study particular risk minimization problems. Finally, we extend our approach to cover general Stochastic Differential games (not necessarily zero-sum), and we obtain similar HJBI equations for the Nash equilibria of such games.
Mariusz Michta - One of the best experts on this subject based on the ideXlab platform.
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On connections between Stochastic Differential inclusions and set-valued Stochastic Differential equations driven by semimartingales
Journal of Differential Equations, 2017Co-Authors: Mariusz MichtaAbstract:Abstract In the paper we study properties of solutions to Stochastic Differential inclusions and set-valued Stochastic Differential equations with respect to semimartingale integrators. We present new connections between their solutions. In particular, we show that attainable sets of solutions to Stochastic inclusions are subsets of values of multivalued solutions of certain set-valued Stochastic equations. We also show that every solution to Stochastic inclusion is a continuous selection of a multivalued solution of an associated set-valued Stochastic equation. The results obtained in the paper generalize results dealing with this topic known both in deterministic and Stochastic cases.
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The interrelation between Stochastic Differential inclusions and set-valued Stochastic Differential equations
Journal of Mathematical Analysis and Applications, 2013Co-Authors: Marek T. Malinowski, Mariusz MichtaAbstract:Abstract In this paper we connect the well established theory of Stochastic Differential inclusions with a new theory of set-valued Stochastic Differential equations. Solutions to the latter equations are understood as continuous mappings taking on their values in the hyperspace of nonempty, bounded, convex and closed subsets of the space L 2 consisting of square integrable random vectors. We show that for the solution X to a set-valued Stochastic Differential equation corresponding to a Stochastic Differential inclusion, there exists a solution x for this inclusion that is a ‖ ⋅ ‖ L 2 -continuous selection of X . This result enables us to draw inferences about the reachable sets of solutions for Stochastic Differential inclusions, as well as to consider the viability problem for Stochastic Differential inclusions.
G. O. S. Ekhaguere - One of the best experts on this subject based on the ideXlab platform.
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Quantum Stochastic Differential inclusions of hypermaximal monotone type
International Journal of Theoretical Physics, 1995Co-Authors: G. O. S. EkhaguereAbstract:In continuation of our study of the existence of solutions of quantum Stochastic Differential inclusions, we first introduce and develop some aspects of the theory of maximal [resp. hypermaximal] monotone multifunctions, including the description of a number of properties of their resolvents and Yosida approximations, in the present noncommutative setting. Then, it is proved that, under a certain continuity assumption, a quantum Stochastic Differential inclusion of hypermaximal monotone type has a unique adapted solution which is obtained as the limit of the unique adapted solutions of a one-parameter family of Lipschitzian quantum Stochastic Differential equations. As examples, we show that a large class of quantum Stochastic Differential inclusions which satisfy the assumptions and conclusion of our main result arises as perturbations of certain quantum Stochastic Differential equations by some multivalued Stochastic processes.
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Lipschitzian quantum Stochastic Differential inclusions
International Journal of Theoretical Physics, 1992Co-Authors: G. O. S. EkhaguereAbstract:Quantum Stochastic Differential inclusions are introduced and studied within the framework of the Hudson-Parthasarathy formulation of quantum Stochastic calculus. Results concerning the existence of solutions of a Lipschitzian quantum Stochastic Differential inclusion and the relationship between the solutions of such an inclusion and those of its convexification are presented. These generalize the Filippov existence theorem and the Filippov-Wažewski relaxation theorem for classical Differential inclusions to the present noncommutative setting.
Michał Kisielewicz - One of the best experts on this subject based on the ideXlab platform.
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Stochastic Differential inclusions
Discussiones Mathematicae. Differential Inclusions Control and Optimization, 2020Co-Authors: Michał KisielewiczAbstract:This chapter is devoted to the theory of Stochastic Differential inclusions. The main results deal with Stochastic functional inclusions defined by set-valued functional Stochastic integrals. Subsequent sections discuss properties of Stochastic and backward Stochastic Differential inclusions.
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Stochastic Differential inclusions and diffusion processes
Journal of Mathematical Analysis and Applications, 2007Co-Authors: Michał KisielewiczAbstract:Connections between weak solutions of Stochastic Differential inclusions and solutions of partial Differential inclusions, generated by given set-valued mappings are considered. The main results are based on some continuous approximation selection theorem and weak compactness of the set of all weak solutions to a given Stochastic Differential inclusion.
Marek T. Malinowski - One of the best experts on this subject based on the ideXlab platform.
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On solutions set of a multivalued Stochastic Differential equation
Czechoslovak Mathematical Journal, 2017Co-Authors: Marek T. Malinowski, Ravi P. AgarwalAbstract:We analyse multivalued Stochastic Differential equations driven by semimartingales. Such equations are understood as the corresponding multivalued Stochastic integral equations. Under suitable conditions, it is shown that the considered multivalued Stochastic Differential equation admits at least one solution. Then we prove that the set of all solutions is closed and bounded.
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The interrelation between Stochastic Differential inclusions and set-valued Stochastic Differential equations
Journal of Mathematical Analysis and Applications, 2013Co-Authors: Marek T. Malinowski, Mariusz MichtaAbstract:Abstract In this paper we connect the well established theory of Stochastic Differential inclusions with a new theory of set-valued Stochastic Differential equations. Solutions to the latter equations are understood as continuous mappings taking on their values in the hyperspace of nonempty, bounded, convex and closed subsets of the space L 2 consisting of square integrable random vectors. We show that for the solution X to a set-valued Stochastic Differential equation corresponding to a Stochastic Differential inclusion, there exists a solution x for this inclusion that is a ‖ ⋅ ‖ L 2 -continuous selection of X . This result enables us to draw inferences about the reachable sets of solutions for Stochastic Differential inclusions, as well as to consider the viability problem for Stochastic Differential inclusions.
