Paper shows L∞-positivity and stochastic completeness are equivalent.
problem Analyzing L∞-positivity preserving property and stochastic completeness. method Using monotone approximation results for distributional solutions of −Δ+1≥0. result The L∞-positivity preserving property is equivalent to stochastic completeness. The paper proves a conjecture about positivity preserving in Riemannian manifolds.
problem Proving positivity preserving for Lp functions on Riemannian manifolds. method New a-priori regularity result, Liouville type theorem, Brezis-Kato inequality.
result Proves a conjecture by M. Braverman, O. Milatovic, and M. Shubin (2002).
The paper proves positivity preservation and self-adjointness for Schrödinger operators on incomplete Riemannian manifolds.
problem Positivity preservation and self-adjointness for Schrödinger-type operators on incomplete Riemannian manifolds.
method Control of potential behavior near the Cauchy boundary, essential self-adjointness proof, core of smooth compactly supported functions.
result Positivity preservation and essential self-adjointness of Schrödinger operators on Lp functions on incomplete Riemannian manifolds. In this note we review some results regarding higher order elliptic differential operators on manifolds without boundary.
Our aim in this note is to extend the semi discrete technique by combine it with the split step method. We apply our new method to the Ait-Sahalia model and propose an explicit and positivity preserving numerical scheme.
The paper proves that under certain conditions, solutions to a specific differential inequality are nonnegative.
problem Preserving positivity of solutions to a differential inequality on Riemannian manifolds.
method Analytic approach using Llocp norms and growth conditions over geodesic balls. result Nonnegative solutions to the inequality −Δu+λu≥0 are preserved under suitable growth conditions. The paper proves conditions for positivity preservation on Riemannian manifolds.
problem Conditions for positivity preservation on Riemannian manifolds.
method Smooth monotonic approximation, subharmonic distributions, and manifold versions of inequalities.
result Conditions for Lp-Positivity Preservation on Riemannian manifolds. Study on positivity properties of vector bundle Monge-Ampère equation.
problem Analyzing positivity in vector bundle Monge-Ampère equation.
method Investigates MA-positivity and MA-semi-positive solutions for different ranks of holomorphic bundles over complex surfaces and manifolds.
result Positivity preservation in rank-two holomorphic bundles but not in higher ranks.
Combines machine learning and convex limiting for accurate subgrid flux modeling in shallow-water equations.
problem Accurate subgrid flux modeling in shallow-water equations.
method Machine learning and flux limiting for property-preserving subgrid scale modeling.
result The proposed method produces meaningful closures even in untrained scenarios.
Two methods improve simulation of European call options under Heston model.
problem Efficient simulation of European call options under Heston model.
method Two strongly convergent and positivity-preserving methods for Cox-Ingersoll-Ross process under Lamperti transformation: truncated Euler and backward Euler methods.
result Explicit truncated Euler method is computationally effective and robust under high volatility, while implicit backward Euler method provides high accuracy and stability.
Diagonal Frog: High-order positivity-preserving FD schemes for anisotropic Fokker-Planck equations
problem Positivity-preserving discretizations for anisotropic Fokker-Planck equations
method Diagonal Frog discretization
result Second-order accuracy and mass conservation
The paper examines functional properties on manifolds with very negative curvature.
problem Functional properties on manifolds with very negative curvature.
method New Hardy-type inequalities and first and second order inequalities.
result Functional properties typically hold in manifolds with polynomially growing negative curvature.
In this work, we propose a new evolving geometric flow (called translating mean curvature flow) for the translating solitons of hypersurfaces in Rn+1. We study the basic properties, such as positivity preserving property, of the translating mean curvature flow. The Dirichlet problem for the graphical translating m…
Study preserves planar and graphical properties of curves under elastic flow.
problem Maintaining planar and graphical properties of non-compact curves under elastic flow.
method Extended recent work on adapted elastic energy to derive thresholds for planar and graphical embeddedness.
result Derived new Li--Yau type inequality for complete planar curves.
Solves Lempert's question on Nakano semi-positivity preservation.
problem Preserving Nakano semi-positivity under limits of metrics.
method Establishes L2 extension theorem and uses multiplier submodule sheaves. result Affirmative solution to Lempert's question on Nakano semi-positivity.
In this paper, we introduce a flow over the projective bundle p:P(E∗)→M, which is a natural generalization of both Hermitian-Yang-Mills flow and Kähler-Ricci flow. We prove that the semipositivity of curvature of the hyperplane line bundle OP(E∗)(1) is preserved along this flow under the null eige…
We derive several new applications of the concept of sequences of Laplacian cut-off functions on Riemannian manifolds (which we prove to exist on geodesically complete Riemannian manifolds with nonnegative Ricci curvature): In particular, we prove that this existence implies Lq-estimates of the gradient, a …
In this paper we want to exploit further the semi-discrete method appeared in Halidias and Stamatiou (2015). We are interested in the numerical solution of mean reverting CEV processes that appear in financial mathematics models and are described as non negative solutions of certain stochastic differential equations wi…
Method shows existence of conformal metrics with constant Q-curvature on manifolds.
problem Existence of conformal metrics with constant Q-curvature on manifolds. method Bahri-Coron barycenter method applied to GJMS operator.
result Existence of positive solutions for the 2k-th order Q-curvature equation. Deep density methods improve filtering in high-dimensional systems.
problem Nonlinear filtering in high-dimensional systems.
method Two deep density methods based on Feynman-Kac formulas and neural networks.
result Logarithmic deep backward stochastic differential equation filter outperforms classical methods in high dimensions.
This paper provides a practical method to extract caplet volatilities from quoted data.
problem Extracting caplet volatilities from quoted data is complex and not straightforward.
method The paper presents a constructive algorithm based on criteria and robust outlier detection. It includes direct interpolation, bootstrap methods, and global search methods.
result The paper introduces methods to extract caplet volatilities that are arbitrage-free and consistent with quoted data.
Compactness of metrics with higher-order constant Q-curvature on manifolds.
problem Investigating compactness of conformal metrics with constant Q-curvature of higher order. method Analyzing solutions of the Q-curvature equation using Juhl's recursive formulae and blow-up analysis. result Established compactness for an arbitrary 1≤k<2n under specific conditions.