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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.

Stochastic Modulation Equations on Unbounded Domains

Bianchi, Luigi A., Blömker, Dirk (2017)

Proceedings of Equadiff 14

We study the impact of small additive space-time white noise on nonlinear stochastic partial differential equations (SPDEs) on unbounded domains close to a bifurcation, where an infinite band of eigenvalues changes stability due to the unboundedness of the underlying domain. Thus we expect not only a slow motion in time, but also a slow spatial modulation of the dominant modes, and we rely on the approximation via modulation or amplitude equations, which acts as a replacement for the lack of random...

Stochastic representations of derivatives of solutions of one-dimensional parabolic variational inequalities with Neumann boundary conditions

Mireille Bossy, Mamadou Cissé, Denis Talay (2011)

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

In this paper we explicit the derivative of the flows of one-dimensional reflected diffusion processes. We then get stochastic representations for derivatives of viscosity solutions of one-dimensional semilinear parabolic partial differential equations and parabolic variational inequalities with Neumann boundary conditions.

Strangely sweeping one-dimensional diffusion

Ryszard Rudnicki (1993)

Annales Polonici Mathematici

Let X(t) be a diffusion process satisfying the stochastic differential equation dX(t) = a(X(t))dW(t) + b(X(t))dt. We analyse the asymptotic behaviour of p(t) = ProbX(t) ≥ 0 as t → ∞ and construct an equation such that l i m s u p t → ∞ t - 1 ∫ 0 t p ( s ) d s = 1 and l i m i n f t → ∞ t - 1 ∫ 0 t p ( s ) d s = 0 .

Strong solutions for stochastic differential equations with jumps

Zenghu Li, Leonid Mytnik (2011)

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

General stochastic equations with jumps are studied. We provide criteria for the uniqueness and existence of strong solutions under non-Lipschitz conditions of Yamada–Watanabe type. The results are applied to stochastic equations driven by spectrally positive Lévy processes.

Superposition rules and stochastic Lie–Scheffers systems

Joan-Andreu Lázaro-Camí, Juan-Pablo Ortega (2009)

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

This paper proves a version for stochastic differential equations of the Lie–Scheffers theorem. This result characterizes the existence of nonlinear superposition rules for the general solution of those equations in terms of the involution properties of the distribution generated by the vector fields that define it. When stated in the particular case of standard deterministic systems, our main theorem improves various aspects of the classical Lie–Scheffers result. We show that the stochastic analog...

Currently displaying 61 – 80 of 104