This paper investigates optimal consumption in the stochastic Ramsey problem with the Cobb-Douglas production function. Contrary to prior studies, we allow for general consumption processes, without any a priori boundedness constraint. A non-standard stochastic differential equation, with neither Lipschitz continuity n…
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48 results for “stochastic boundedness”
Paper proves convergence of SA algorithm via martingale and converse Lyapunov methods.
problem Proves convergence of stochastic approximation algorithm.
method Uses martingale and converse Lyapunov methods to prove convergence.
result Provides alternate proof of convergence for SA algorithm.
We provide sufficient conditions for the existence and uniqueness of solutions to a stochastic differential equation which arises in a price impact model. These conditions are stated as smoothness and boundedness requirements on utility functions or Malliavin differentiability of payoffs and endowments.
New algorithms improve distributed optimization under mild variance conditions.
problem Improving distributed optimization for large-scale machine learning problems.
method Revisited Federated Averaging and SCAFFOLD algorithms under a general variance condition.
result Established convergence results for smooth nonconvex objective functions under mild variance conditions.
The study provides statistical guarantees for Bayesian variational boosting.
problem Statistical and convergence issues in variational boosting.
method Proposed a novel variational family and a functional Frank-Wolfe optimization algorithm.
result Demonstrated stochastic boundedness and provided convergence rate for boosting iterates.
New bounds for neural networks without loss boundedness assumption.
problem Generalization error bounds for two-layer neural networks.
method Wasserstein distance estimates and moment bounds for stochastic gradient method.
result Dimension-free rate of order for independent test data.
Stochastic gradient descent (SGD) is a popular and efficient method with wide applications in training deep neural nets and other nonconvex models. While the behavior of SGD is well understood in the convex learning setting, the existing theoretical results for SGD applied to nonconvex objective functions are far from …
Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operatorsstat.ML
Paper develops SINNOs for approximating stochastic processes.
problem Approximating stochastic processes with neural networks.
method Developed stochastic interpolation neural network operators (SINNOs) with random coefficients.
result Established boundedness, interpolation accuracy, and approximation capabilities of SINNOs.
Convergence Analysis of a Momentum Algorithm with Adaptive Step Size for Non Convex Optimizationmath.OC
Although ADAM is a very popular algorithm for optimizing the weights of neural networks, it has been recently shown that it can diverge even in simple convex optimization examples. Several variants of ADAM have been proposed to circumvent this convergence issue. In this work, we study the ADAM algorithm for smooth nonc…
The paper studies boundedness of pseudo-differential operators on smooth manifolds.
problem Boundedness of pseudo-differential operators in - spaces on smooth manifolds.
method Using global symbols and extending Hörmander's condition, the paper investigates -boundedness, - estimates, and - boundedness for Fourier multipliers and pseudo-differential operators.
result The paper proves - boundedness for the range .
Study proves boundedness of operators in variable exponent Morrey spaces.
problem Boundedness of operators in global Morrey-type spaces with variable exponents.
method Analysis of Hardy-Littlewood maximal operator and potential type operator in variable exponent Morrey spaces.
result Boundedness of the Hardy-Littlewood maximal operator and potential type operator in global Morrey-type spaces with variable exponents.
On the Interplay Between Hodge Projections and Bounded Harmonic Functions on Manifolds with Endsmath.AP
Study examines -boundedness of Hodge projection on manifolds with ends.
problem Understanding -boundedness of Hodge projection on manifolds with ends.
method Investigates the relationship between Hodge projection, Riesz transform, and bounded harmonic functions.
result Connects -boundedness of Hodge projection to the structure of harmonic one-forms and bounded harmonic functions.
The study shows boundedness and constructs a moduli space for Calabi-Yau fibrations.
problem Boundedness and moduli spaces of K-stable Calabi-Yau fibrations over curves.
method Fixed volumes and Iitaka volumes of general fibers, adiabatic sense construction.
result Constructs a separated coarse moduli space of K-stable Calabi-Yau fibrations.
Characterizes Schrödinger operator boundedness on weighted Riemannian manifolds.
problem Classifying functions for bounded Schrödinger operator .
method Investigates weighted -boundedness of Hodge projector.
result Characterizes function for Schrödinger operator boundedness.
Study examines boundedness of oscillating singular integrals on specific Lie groups.
problem Investigating boundedness of oscillating singular integrals on Lie groups of polynomial growth.
method Presented kernel criteria in terms of sub-Riemannian structure and Fourier analysis.
result Extended classical oscillating conditions for boundedness of oscillating convolution operators.
Unified error analysis for discrete flow models.
problem Error analysis of discrete flow models.
method Stochastic calculus theory, Girsanov theorem, generator matching, uniformization.
result First error analysis for discrete flow models.
The paper relaxes assumptions for analyzing stochastic optimization algorithms.
problem Analyzing the convergence of stochastic gradient algorithms under weaker variance assumptions.
method Building on and extending a connection to the Halpern iteration, the paper analyzes algorithms for convex nonsmooth optimization and min-max problems.
result Rates for optimality measures are obtained without requiring boundedness of the feasible set for problems beyond simple constrained optimization.
This paper proves geodesic curvature measures are bounded for curves near cross cap singularities.
problem Boundedness of geodesic curvature measures near cross cap singularities.
method Analyzes intrinsic cross cap singularities and extends Gauss-Bonnet formula.
result Proves boundedness of geodesic curvature measures for curves near cross cap singularities.
Paper refines Chen-Cheng's estimates for Kähler metrics.
problem Uniform boundedness of scalar curvature assumption.
method Replacing uniform boundedness with -boundedness.
result Improved estimates for Kähler metrics under -boundedness.
Paper presents a novel method to assess boundedness and stability of nonlinear systems with variable delays.
problem Challenges in assessing boundedness and stability of vector nonlinear systems with variable delays and coefficients.
method Develops a novel framework to evaluate the evolution of solution norms in such systems by constructing scalar counterparts.
result Introduces new criteria for boundedness and stability and estimates the radii of containing balls for history functions.
Study on flat connections with controlled irregularity.
problem Boundedness of algebraic flat connections with limited irregularity.
method Analysis of families of algebraic flat connections and holonomic D-modules.
result Established boundedness of families of algebraic flat connections with controlled irregularity.
Study confirms boundedness of certain singularities in log Fano geometry.
problem Boundedness of log Fano cone singularities and minimal log discrepancies.
method Analyzing local volumes and minimal log discrepancies of Kollár components.
result Boundedness of K-semistable log Fano cone singularities confirmed in dimension three.
We establish a general "boundedness implies convergence" principle for a family of evolving Riemannian metrics. We then apply this principle to collapsing Calabi-Yau metrics and normalized Kähler-Ricci flows on torus fibered minimal models to obtain convergence results.
Paper characterizes foliated bundle classes via quasi-morphisms and studies their boundedness.
problem Characterizing bounded characteristic classes of foliated bundles.
method Using non-descendible quasi-morphisms on the universal covering of the structure group.
result Non-existence of foliated structures on some Hamiltonian fibrations and non-triviality of the second bounded cohomology group.
The paper proves boundedness of a Riesz transform on weighted manifolds.
problem Establishing \(L^p\)-boundedness of the covariant Riesz transform on differential forms.
method Heat-kernel criterion, volume doubling, heat kernel estimates, curvature control, gradient bounds.
result The covariant Riesz transform is \(L^p\)-bounded for \(p>2\) on weighted Riemannian manifolds.
Let be a complete non-compact Riemannian manifold. In this paper, we derive sufficient conditions on metric perturbation for stability of -boundedness of the Riesz transform, . We also provide counter-examples regarding in-stability for -boundedness of Riesz transform.
New formulation tackles arbitrage in volatile markets using eigenvalue bounds.
problem Arbitrage opportunities in volatile markets beyond a certain time horizon.
method Formulated as a stochastic optimal control problem, solved via PDE.
result Characterized arbitrage time horizon through PDE solution.
We prove that a Ricci flow cannot develop a finite time singularity assuming the boundedness of a suitable space-time integral norm of the curvature tensor. Moreover, the extensibility of the flow is proved under a Ricci lower bound and the boundedness of a space-time integral norm of the scalar curvature.
We give a characterization of relative Ding stable toric Fano manifolds in terms of the behavior of the modified Ding functional. We call the corresponding behavior of the modified Ding functional the pseudo-boundedness from below. We also discuss the pseudo-boundedness of the Ding / Mabuchi functional of general Fano …
The paper analyzes reg-SGD for convex problems, proving convergence and quantifying the rate of convergence.
problem Minimizing convex, L-smooth functions in a Hilbert space.
method Regularized stochastic gradient descent with decaying regularization.
result Strong convergence to the minimum-norm solution without boundedness assumptions.
The study shows boundedness of certain fibered varieties in algebraic geometry.
problem Bounding fibered varieties in algebraic geometry.
method Analyzing Calabi-Yau varieties and their fibrations by abelian or symplectic varieties.
result There are only finitely many deformation classes of certain fibered varieties.
Study boundedness of Riesz transform on differential forms for certain manifolds.
problem Investigate -boundedness of the covariant Riesz transform on differential forms.
method Analyze -boundedness on weighted Riemannian manifolds under curvature-dimension and lower bound conditions.
result Derive Calderón-Zygmund inequality for under curvature-dimension condition.
Boundedness of geometric invariants near a singularity which is a suspension of a singular curvemath.DG
The paper examines geometric invariants near a specific type of singular point.
problem The behavior of geometric invariants near a singular point of a surface or curve.
method Analysis of geometric invariants for surfaces and curves that are suspensions of singular curves.
result Evaluation of the orders of Gaussian and mean curvatures for the studied surfaces and curves.
New deep learning method solves stochastic control problems.
problem Solving strongly coupled FBSDEs for stochastic control.
method Modified deep BSDE method with new loss function.
result Empirical convergence of the new method for three problems.
Uniform TD(0) bound derived for function approximation with Markov noise.
problem Uniform concentration bound for TD(0) with function approximation.
method Contractive stochastic approximation, martingale and Markov noises, Poisson equation, relaxed concentration inequalities.
result Uniform all-time concentration bound for TD(0) with linear function approximation.
Let , where is a stratified group and acts on via automorphic dilations. Homogeneous sub-Laplacians on and can be lifted to left-invariant operators on and their sum is a sub-Laplacian on . Here we prove weak type , -boundedness for …
We undertake a study of markets from the perspective of a financial agent with limited access to information. The set of wealth processes available to the agent is structured with reasonable economic properties, instead of the usual practice of taking it to consist of stochastic integrals against a semimartingale integ…
We consider a structural stochastic volatility model for the loss from a large portfolio of credit risky assets. Both the asset value and the volatility processes are correlated through systemic Brownian motions, with default determined by the asset value reaching a lower boundary. We prove that if our volatility model…
Local positive definite Z2^n-superfunctions can be extended.
problem Bounding and extending local positive definite Z2^n-superfunctions.
method Defining boundedness for Z2^n-superfunctions and extending them.
result Local positive definite Z2^n-superfunctions have positive definite extensions.
Study on curvature invariants near singularities of wavefronts.
problem Conditions for extendibility and boundedness of curvature invariants.
method Investigation of Gaussian curvature, Mean curvature, and principal curvatures near singularities.
result Relationship between convergence to infinity and uniform approximation of fronts.
The paper examines the boundedness of bundle diffeomorphism groups over a circle.
problem Investigating the boundedness of bundle diffeomorphism groups over a circle.
method Distinguishing an integer k and constructing a function to analyze the bundle diffeomorphism group.
result The bundle diffeomorphism group is uniformly perfect when k ≥ 1 and unbounded when k = 0.
The paper examines boundedness of diffeomorphism groups of manifold pairs, focusing on the circle case.
problem Boundedness of conjugation invariant norms on diffeomorphism groups of manifold pairs.
method Analyzes the relation among norms, uses quasimorphisms and rotation angles to derive bounds.
result The diffeomorphism group is uniformly weakly simple and bounded when .
We prove boundedness and polynomial decay statements for solutions to the spin Teukolsky-type equation projected to the spherical harmonic on Reissner-Nordström spacetime. The equation is verified by a gauge-invariant quantity which we identify and which involves the electromagnetic and curvature tensor…
Proves boundedness of log Fano cone singularities with bounded local volumes.
problem Understanding the boundedness of log Fano cone singularities.
method Analyzes K-semistable log Fano cone singularities with bounded volumes.
result The set of local volumes of klt singularities has zero as the only accumulation point.
We consider Kerr spacetimes with parameters a and M such that |a|<< M, Kerr-Newman spacetimes with parameters |Q|<< M, |a|<< M, and more generally, stationary axisymmetric black hole exterior spacetimes which are sufficiently close to a Schwarzschild metric with parameter M>0, with appropriate geometric assumptions on …
Stochastic Multi-level Composition Optimization Algorithms with Level-Independent Convergence Ratesmath.OC
New algorithms solve complex multi-level optimization problems with improved efficiency.
problem Smooth stochastic multi-level composition optimization problems.
method Two algorithms using moving-average and linearized stochastic estimates.
result Achieved sample complexities of O(1/ε^4) and O(1/ε^6).
The paper proves boundedness and decay of Teukolsky equations on Kerr backgrounds.
problem Analyzing boundedness and decay of Teukolsky equations on Kerr backgrounds.
method Adapting techniques from scalar waves, uniform-in-frequency estimates for Teukolsky PDEs were obtained.
result Solutions of Teukolsky equation on subextremal Kerr backgrounds remain bounded and decay in time.
This paper optimizes dividend payout rates with a drawdown constraint in a stochastic model.
problem Optimizing dividend payout rates while avoiding drawdowns in a stochastic model.
method Solving a path-dependent stochastic control problem using Hamilton-Jacobi-Bellman equations and PDE methods.
result Explicit characterization of an optimal feedback control strategy, including two free boundaries and the running maximum surplus process.