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Abstract. We use Yosida approximation to find an Itô formula for mild solutions {X x (t), t ≥ 0} of SPDEs with Gaussian and non-Gaussian coloured noise, the non Gaussian noise being defined through compensated Poisson random measure associated to a Lévy process. The functions to which we apply such Itô formula are in C 1,2 ([0, T ] × H), as in the case considered for SDEs in [19]. Using this Itô formula we prove exponential stability and exponential ultimate boundedness properties in mean square sense for mild solutions. We also compare such Itô formula to an Itô formula for mild solutions introduced by Ichikawa in [15], and an Itô formula written in terms of the semigroup of the drift operator [6] which we extend before to the non Gaussian case.

Several results concerning the existence and uniqueness of solutions of Ito SDE's in a real separable Hubert space have recently been reported. In this work we first obtain the existence and uniqueness of strong solutions to (not necessarily) Ito SDE's in a Hubert space under Lipschitz-type conditions on the coefficients. We assume usual continuity and linear growth conditions. For non-Lipschitz coefficients an approximation technique of Gikhman and Skorokhod is then used to prove the existence of weak solutions taking values in a larger Hubert space H-\. This result depends on an assumption that H can be compactly embedded in H-\, such that the coefficients satisfy regularity conditions with respect to H-\. This assumption is not a limitation to our method as it is necessary even in the deterministic case. Additionally, we prove the existence of martingale solutions to infinite dimensional semilinear SDE's. In both cases, coefficients F(£, ·) and J9(£, ·) may depend on the entire past of X £ C([0, T], H) and not on the value of x(t) alone.Brought to you by | provisional account Unauthenticated Download Date | 7/2/15 1:26 AM

Ample research has identified several features of a learning experience likely to enhance student learning, including collaboration, open-ended exploration, and problem-based learning in real-life scenarios. Missing is a model of how instructors might combine these elements into a single project that works flexibly across disciplines and institutions. This article fills this gap by offering such a model and reporting on its effectiveness in fostering student engagement. It describes a project that instructors at four colleges and universities in Flint, Michigan (USA) piloted during the height of the Flint water crisis. The project asked students to apply class content to the real-world problem unfolding around them, and offered students an opportunity to collaborate with peers. We collected qualitative and quantitative data on students' reactions to the project, and found that the project succeeded in engaging students. We offer recommendations for how instructors can create similar projects in their own classrooms.

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