All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 70 Next

Displaying 1381 – 1400 of 1721

Showing per page

Stochastic differential equations with Sobolev drifts and driven by α -stable processes

Xicheng Zhang (2013)

Annales de l'I.H.P. Probabilités et statistiques

In this article we prove the pathwise uniqueness for stochastic differential equations in ℝ d with time-dependent Sobolev drifts, and driven by symmetric α -stable processes provided that α ∈ ( 1 , 2 ) and its spectral measure is non-degenerate. In particular, the drift is allowed to have jump discontinuity when α ∈ ( 2 d d + 1 , 2 ) . Our proof is based on some estimates of Krylov’s type for purely discontinuous semimartingales.

Stochastic diffrential equations on Banach spaces and their optimal feedback control

(2012)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider stochastic differential equations on Banach spaces (not Hilbert). The system is semilinear and the principal operator generating a C₀-semigroup is perturbed by a class of bounded linear operators considered as feedback operators from an admissible set. We consider the corresponding family of measure valued functions and present sufficient conditions for weak compactness. Then we consider applications of this result to several interesting optimal feedback control problems....

Stochastic evolution equations driven by Liouville fractional Brownian motion

Zdzisław Brzeźniak, Jan van Neerven, Donna Salopek (2012)

Czechoslovak Mathematical Journal

Let H be a Hilbert space and E a Banach space. We set up a theory of stochastic integration of ℒ ( H , E ) -valued functions with respect to H -cylindrical Liouville fractional Brownian motion with arbitrary Hurst parameter 0 < β < 1 . For 0 < β < 1 2 we show that a function Φ : ( 0 , T ) → ℒ ( H , E ) is stochastically integrable with respect to an H -cylindrical Liouville fractional Brownian motion if and only if it is stochastically integrable with respect to an H -cylindrical fractional Brownian motion. We apply our results to stochastic evolution equations...

Stochastic evolution equations on Hilbert spaces with partially observed relaxed controls and their necessary conditions of optimality

N.U. Ahmed (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider the question of optimal control for a class of stochastic evolution equations on infinite dimensional Hilbert spaces with controls appearing in both the drift and the diffusion operators. We consider relaxed controls (measure valued random processes) and briefly present some results on the question of existence of mild solutions including their regularity followed by a result on existence of partially observed optimal relaxed controls. Then we develop the necessary conditions...

Stochastic flow for SDEs with jumps and irregular drift term

Enrico Priola (2015)

Banach Center Publications

We consider non-degenerate SDEs with a β-Hölder continuous and bounded drift term and driven by a Lévy noise L which is of α-stable type. If β > 1 - α/2 and α ∈ [1,2), we show pathwise uniqueness and existence of a stochastic flow. We follow the approach of [Priola, Osaka J. Math. 2012] improving the assumptions on the noise L. In our previous paper L was assumed to be non-degenerate, α-stable and symmetric. Here we can also recover relativistic and truncated stable processes and some classes...

Stochastic fuzzy differential equations with an application

Marek T. Malinowski, Mariusz Michta (2011)

Kybernetika

In this paper we present the existence and uniqueness of solutions to the stochastic fuzzy differential equations driven by Brownian motion. The continuous dependence on initial condition and stability properties are also established. As an example of application we use some stochastic fuzzy differential equation in a model of population dynamics.

Currently displaying 1381 – 1400 of 1721