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Controlled McKean-Vlasov stochastic differential equations

Forward-Backward Stochastic Differential Equations and Controlled McKean Vlasov Dynamics

Forward-Backward Stochastic Differential Equations and Controlled McKean Vlasov Dynamics

... the stochastic Pontryagin maximum principle that is tailor-made to McKean- Vlasov dynamics and give sufficient conditions for existence of an optimal ...Backward Stochastic Differential ...

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Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics

Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics

... a stochastic control problem where the conditional law P W 0 X t is the sole controlled state variable driven by the random noise W 0 , and by showing the continuity of the value function in the Wasserstein ...

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Control of McKean-Vlasov systems and applications

Control of McKean-Vlasov systems and applications

... the stochastic maximum principle for characterizing solutions to the controlled McKean-Vlasov systems in terms of adjoint backward stochastic differential equations ...

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Control of McKean-Vlasov Dynamics versus Mean Field Games

Control of McKean-Vlasov Dynamics versus Mean Field Games

... of stochastic differential games with a finite number of players as the number of players tends to the ...over controlled dynamics of McKean-Vlasov ...forward-backward stochastic ...

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Fully nonlinear stochastic partial differential equations: non-smooth equations and applications

Fully nonlinear stochastic partial differential equations: non-smooth equations and applications

... In spite of their importance very little was known for equations like (0.1) even for smooth H before [LS1], with the exception of the uniformly elliptic linear theory, i.e., when both F and H are linear and F is ...

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Degenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case

Degenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case

... the flux term. Such equations, in the first-order case, have been studied recently by Lions, Perthame and Souganidis, [ 19 , 20 ]. In comparison to the previous works of the authors [ 7 ] and [ 12 ], the present ...

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A Stochastic Particle Method with Random Weights for the Computation of Statistical Solutions of McKean-Vlasov Equations. Part II: Convergence Rate of The Method

A Stochastic Particle Method with Random Weights for the Computation of Statistical Solutions of McKean-Vlasov Equations. Part II: Convergence Rate of The Method

... Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex France Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - [r] ...

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Backward Stochastic Differential Equations with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations

Backward Stochastic Differential Equations with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations

... Since the pioneering work of [29], in the Brownian case, the relations between more general BSDEs and associated deterministic problems have been studied extensively, and innovations have been made in several directions. ...

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On the discretization of backward doubly stochastic differential equations

On the discretization of backward doubly stochastic differential equations

... of stochastic differential equations Springer (1999) [MY99] Ma ...Forward-Backward Stochastic Differential Equations and their Applications Lecture Note in ...parabolic ...

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NUMERICAL METHOD FOR FBSDES OF MCKEAN-VLASOV TYPE

NUMERICAL METHOD FOR FBSDES OF MCKEAN-VLASOV TYPE

... the second component is infinite dimensional makes intractable the complexity of these approaches. To avoid any similar problem, we use a pathwise approach for the forward component; it consists in iterating successively ...

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Stochastic partial differential equations with singular terminal condition

Stochastic partial differential equations with singular terminal condition

... These equations appear naturally in various applications as for instance, Zakai equation in filtering ([26, 27]), in pathwise stochastic control theory or stochastic control with partial observations ...

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Backward stochastic differential equations and stochastic control and applications to mathematical finance

Backward stochastic differential equations and stochastic control and applications to mathematical finance

... of stochastic control problems in the filtration F, and this is achieved by assuming the existence of a condi- tional density on the default times given the default-free information ...this stochastic ...

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Some contributions to stochastic control and backward stochastic differential equations in finance.

Some contributions to stochastic control and backward stochastic differential equations in finance.

... Faisons maintenant une revue rapide des mod`eles principaux de taux. Certains mod`eles pr´ef`erent mod´eliser directement le taux court. C’est la cas entre autres du mod`ele de Vasicek ou de Ho et Lee parmi les plus c´e- ...

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Development of geostatistical models using Stochastic Partial Differential Equations

Development of geostatistical models using Stochastic Partial Differential Equations

... equation, we show that there exists a great variety of stationary models which satisfy spatio-temporally its homogeneous form, and which can be chosen to follow an arbitrary spatial covariance behaviour. We call these ...

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Development of geostatistical models using stochastic partial differential equations

Development of geostatistical models using stochastic partial differential equations

... equation, we show that there exists a great variety of stationary models which satisfy spatio-temporally its homogeneous form, and which can be chosen to follow an arbitrary spatial covariance behaviour. We call these ...

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On Multidimensional stable-driven Stochastic Differential Equations with Besov drift

On Multidimensional stable-driven Stochastic Differential Equations with Besov drift

... Corollary 7 (Zvonkin type theory for the mollified PDE). In particular, the condition θ > 1 provides a pointwise gradient estimate for the solution of the mollified PDE. Of course, to[r] ...

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The Euler Scheme for Lévy driven Stochastic Differential Equations

The Euler Scheme for Lévy driven Stochastic Differential Equations

... Unite´ de recherche INRIA Lorraine, Technopoˆle de Nancy-Brabois, Campus scientifique, 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LE` S NANCY Unite´ de recherche INRIA Rennes, Ir[r] ...

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Numerical approximation of Backward Stochastic Differential Equations with Jumps

Numerical approximation of Backward Stochastic Differential Equations with Jumps

... ward stochastic differential equation with jumps in a discrete stochastic basis with a filtration generated by two independent, centered random ...

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A new McKean-Vlasov stochastic interpretation of the parabolic-parabolic Keller-Segel model: The one-dimensional case

A new McKean-Vlasov stochastic interpretation of the parabolic-parabolic Keller-Segel model: The one-dimensional case

... new McKean-Vlasov stochastic interpretation of the parabolic-parabolic Keller-Segel model: The one-dimensional ...a stochastic interpretation of the one-dimensional parabolic-parabolic ...

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The inverse problem for rough controlled differential equations

The inverse problem for rough controlled differential equations

... solution map, which associates to the starting point x 0 and the rough path (X, X) the solution x • , is continuous. This is in stark contrast with the fact that solutions of stochastic differential ...

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