A Markov approach to credit rating migration conditional on economic states
Canadian Journal of Statistics, EarlyView.Abstract We develop a model for credit rating migration that accounts for the impact of economic state fluctuations on default probabilities. The joint process for the economic state and the rating is modelled as a time‐homogeneous Markov chain. While the rating process itself possesses the Markov property only under restrictive conditions, methods ...
Michael Kalkbrener, Natalie Packham
wiley +1 more source
$q$-Analogues of the Sums of Consecutive Integers, Squares, Cubes, Quarts and Quints [PDF]
, 2004 Michael J. Schlosser
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Isoperimetric inequalities on slabs with applications to cubes and Gaussian slabs
Communications on Pure and Applied Mathematics, EarlyView.Abstract We study isoperimetric inequalities on “slabs”, namely weighted Riemannian manifolds obtained as the product of the uniform measure on a finite length interval with a codimension‐one base. As our two main applications, we consider the case when the base is the flat torus R2/2Z2$\mathbb {R}^2 / 2 \mathbb {Z}^2$ and the standard Gaussian measure
Emanuel Milman
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Degree theory for 4‐dimensional asymptotically conical gradient expanding solitons
Communications on Pure and Applied Mathematics, EarlyView.Abstract We develop a new degree theory for 4‐dimensional, asymptotically conical gradient expanding solitons. Our theory implies the existence of gradient expanding solitons that are asymptotic to any given cone over S3$S^3$ with non‐negative scalar curvature. We also obtain a similar existence result for cones whose link is diffeomorphic to S3/Γ$S^3/\
Richard H. Bamler, Eric Chen
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Sequences, q-Multinomial Identities, Generalized Galois Numbers, and Integer Partitions with Kinds [PDF]
, 2019 Adrian Avalos, Mark Bly
openalex
A priori bounds for the generalised parabolic Anderson model
Communications on Pure and Applied Mathematics, EarlyView.Abstract We show a priori bounds for solutions to (∂t−Δ)u=σ(u)ξ$(\partial _t - \Delta) u = \sigma (u) \xi$ in finite volume in the framework of Hairer's Regularity Structures [Invent Math 198:269–504, 2014]. We assume σ∈Cb2(R)$\sigma \in C_b^2 (\mathbb {R})$ and that ξ$\xi$ is of negative Hölder regularity of order −1−κ$- 1 - \kappa$ where κ<κ¯$\kappa <
Ajay Chandra +2 more
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A positivity conjecture for a quotient of <i>q</i>-binomial coefficients. [PDF]
Ramanujan JGatzweiler M, Krattenthaler C.
europepmc +1 more source
Some approximation results on Bleimann-Butzer-Hahn operators defined by (p,q)-integers
, 2016 M. Mursaleen +3 more
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TimeFlow 2: An Unsupervised Cell Lineage Detection Method for Flow Cytometry Data
Cytometry Part A, EarlyView.TimeFlow 2 is a new method for cell lineage inference in flow cytometry data. It constructs cell state paths along pseudotime and aggregates them into biologically informative groups. It allows tracking of cytometry markers within each automatically inferred lineage.
Margarita Liarou +2 more
wiley +1 more source
Multilateral transformations of q-series with quotients of parameters that are nonnegative integer powers of q [PDF]
, 2001 Michael J. Schlosser
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