Proves weak convergence equals mean convergence in GGC.
problem Proving convergence in GGC distributions.
method Using generalized gamma convolution (GGC) and expected utility maximization.
result Weak convergence implies mean convergence in GGC.
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48 results for “Weak convergence”
Sharp bounds on weak convergence rate for rough volatility models.
problem Understanding the convergence rate in discretizing rough volatility models.
method Analyzing general and linear models to derive bounds.
result Sharper bound of \(H + 1/2\) for linear models.
Studied SGD convergence under weak conditions.
problem Convergence of SGD in nonconvex optimization.
method Analyzed biased nonconvex SGD under mild conditions.
result Provided convergence rates and complexities.
The paper shows how MMD metrizes weak convergence for certain kernels.
problem Characterizing MMD metrizing weak convergence for a wide class of kernels.
method Proving MMD metrizes weak convergence for specific kernels on a locally compact space.
result Corrected prior results and identified new kernels metrizing weak convergence.
In this paper we study utility maximization with proportional transaction costs. Assuming extended weak convergence of the underlying processes we prove the convergence of the corresponding utility maximization problems. Moreover, we establish a limit theorem for the optimal trading strategies. The proofs are based on …
Proves curvature tensor convergence for smoothable spaces.
problem Curvature tensor behavior in smoothable Alexandrov spaces.
method Weak convergence of curvature tensors in noncollapsing sequences.
result Proves convergence of curvature tensors in smoothable Alexandrov spaces.
Convergence of the financial value of weak information for a sequence of discrete-time marketsmath.PR
Study shows financial value of weak information converges in discrete vs continuous markets.
problem Analyzing financial value of weak information in discrete vs continuous markets.
method Defined minimal probability measure and financial value of weak information, then showed convergence.
result Financial value of weak information converges in discrete vs continuous markets.
Study approximates weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
problem Approximating weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
method Used Euler type scheme with integrated kernels to study weak convergence rate.
result Obtained weak convergence rate of for discretised rough Ornstein-Uhlenbeck process and stochastic rough volatility model.
In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong convergence. We exemplify thi…
Paper proposes an algorithm to recover full supervision from weakly labeled data.
problem Machine learning requires expensive data annotation, motivating the use of weak supervision.
method The paper introduces a disambiguation principle and an empirical disambiguation algorithm for partial labelling.
result The algorithm achieves exponential convergence rates under learnability assumptions.
Neural networks trained with actor-critic algorithms converge to ODEs under weak convergence analysis.
problem Challenges in convergence analysis due to changing data distributions in online learning.
method Geometric ergodicity of data samples, Poisson equation, weak convergence techniques.
result Actor and critic networks converge to solutions of ODEs with random initial conditions.
Preserves scalar curvature bounds under weak convergence of 3-manifolds.
problem Preserving scalar curvature bounds under weak convergence of 3-manifolds.
method Comparison between μ-bubbles in M_k and M.
result Scalar curvature lower bounds are preserved under weak convergence.
Stability of Yang-Mills connections' Morse indices and nullity in 4D.
problem Stability of Yang-Mills connections' Morse indices and nullity in 4D under weak convergence.
method Proves stability results of the Morse index plus nullity of Yang-Mills connections in dimension 4 under weak convergence.
result Stability of the sum of Morse indices and nullity of a sequence of Yang-Mills connections.
In this paper, we prove that a sequence of weak almost Kähler-Ricci solitons under further suitable conditions converge to a Kähler-Ricci soliton with complex codimension of singularities at least 2 in the Gromov-Hausdorff topology. As a corollary, we show that on a Fano manifold with the modified K-energy bounded belo…
In this paper we find tight sufficient conditions for the continuity of the value of the utility maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We also establish a weak convergence result for the terminal wealths of the optimal portfolios. Finally,…
Paper studies identifiability and stability of drifting fields in generative modeling.
problem Identify and stabilize drifting fields in generative modeling.
method Introduces companion-elliptic kernel families to address limitations of Laplace kernel.
result Establishes field identifiability and demonstrates scalar observables for weak convergence.
Study on error rates for approximating rough volatility models.
problem Simulation of rough volatility models with fractional Brownian motion.
method Analysis of weak error rates for numerical schemes, focusing on fBm and cubic test functions.
result Convergence rates for approximations are for exact left-point discretization and for hybrid schemes.
LMC algorithm receives first convergence guarantees under weak smoothness conditions.
problem Convergence guarantees for LMC under weak smoothness conditions.
method Using Latała--Oleszkiewicz or modified log-Sobolev inequalities.
result First convergence guarantees for LMC under weak smoothness conditions.
The paper explores identifiability and stability in drifting fields using companion-elliptic kernels.
problem Identifying and stabilizing drifting fields in generative modeling.
method Introduces companion-elliptic kernel families and analyzes their properties to address identifiability and stability issues.
result Established field identifiability for arbitrary Borel probability measures and demonstrated that field convergence alone does not guarantee weak convergence.
Centralized systemic risk control in the interbank system: Weak formulation and Gamma-convergencemath.OC
Paper studies central bank's strategy to control systemic risk in interbank system.
problem Minimizing average distance between log-monetary reserves and target levels.
method Weak formulation, Ekeland's variational principle, Gamma-convergence, stochastic Fokker-Planck-Kolmogorov equation.
result Proves convergence of optimal strategies as number of banks increases.
New KSDs control moments in approximations, improving diagnostics and tests.
problem Inability of standard KSDs to control moment convergence.
method Developed alternative diffusion KSDs under sufficient conditions.
result First KSDs to exactly characterize q-Wasserstein convergence.
Study rough volatility models using path-dependent PDEs and fractional Brownian motions.
problem Modeling and analyzing rough volatility in financial markets.
method Showed conditional expectations are unique classical solutions to path-dependent PDEs derived from functional Itô formula. Leverage these to study weak rates of convergence for discretized stochastic integrals.
result Obtained optimal weak error rates for approximating log-stock prices in rough volatility models.
Paper introduces HRPCFD for efficient training of stochastic processes.
problem Discontinuities in stochastic processes over time.
method High Rank Path Development method and HRPCFD metric.
result Efficient algorithm for training HRPCFD from data.
The paper proves stability of critical points for conformally invariant Lagrangians.
problem Stability of critical points for conformally invariant Lagrangians under weak convergence.
method Upper-semi-continuity of Morse index plus nullity established for critical points.
result The sum of Morse indices and nullity is bounded from above by the sum of the Morse indices plus the nullity of the weak limit and bubbles.
Proves existence and uniqueness of weak solutions for specific equations.
problem Existence and uniqueness of solutions for generalized Monge-Ampère and deformed Hermitian-Yang-Mills equations.
method Combines viscosity-theoretic and pluripotential-theoretic techniques.
result Existence and uniqueness of weak solutions in boundary cases.
The paper studies limits of flows on Kähler surfaces, proving convergence to solutions of equations.
problem Analyzing limits of flows on Kähler surfaces and their convergence to solutions of equations.
method Using a property of limits of viscosity subsolutions.
result Proves convergence of flows to weak solutions of the Monge-Ampère equation.
In this paper we generalize the framework of the feasible descent method (FDM) to a randomized (R-FDM) and a coordinate-wise random feasible descent method (RC-FDM) framework. We show that the famous SDCA algorithm for optimizing the SVM dual problem, or the stochastic coordinate descent method for the LASSO problem, f…
Estimates ends of Ricci shrinkers, focusing on smooth and singular cases.
problem Understanding the structure of ends in Ricci shrinkers, especially singular ones.
method Analyzes general and asymptotically conical ends, applies to weak convergence.
result No new conical end can form in the limit of sequences of Ricci shrinkers.
Establishes a microstructural foundation for a rough log-normal volatility model.
problem Developing a robust model for financial volatility under microstructural effects.
method Introduced a sequence of order-driven financial market models with Poisson process arrivals and analyzed their convergence to a log-normal rough volatility model.
result Weak convergence of price-volatility process to a log-normal rough volatility model with established weak error rates.
In this paper we consider Dynkin's games with payoffs which are functions of an underlying process. Assuming extended weak convergence of underlying processes to a limit process we prove convergence Dynkin's games values corresponding to to the Dynkin's game…
On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regimemath.AP
Gradient descent converges to minimum Bayes risk for two-layer ReLU networks in mean field regime.
problem Training two-layer ReLU networks using gradient descent in the mean field regime.
method Describes a condition for convergence to minimum Bayes risk, extending previous results to ReLU-activated networks.
result The condition for convergence does not depend on initialization and concerns weak convergence of network realization.
We investigate the computational aspects of the basket CDS pricing with counterparty risk under a credit contagion model of multinames. This model enables us to capture the systematic volatility increases in the market triggered by a particular bankruptcy. The drawback of this problem is its analytical complication due…
Improved volatility models for option pricing with weak error rates.
problem Improving volatility models to fit market data better.
method Developed a weak convergence analysis for the Euler method applied to linear rough volatility models.
result Proved weak convergence rates of 1/2 + H for linear models and 1 for quadratic payoffs.
In this paper, we prove that on a Fano manifold which admits a Kähler-Ricci soliton $(\om,X)$, if the initial Kähler metric $\om_{\vphi_0}$ is close to $\om$ in some weak sense, then the weak Kähler-Ricci flow exists globally and converges in Cheeger-Gromov sense. Moreover, if $\vphi_0$ is also -invariant, the…
We prove existence and regularity of minimisers for the Canham-Helfrich energy in the class of weak (possibly branched and bubbled) immersions of the -sphere. This solves (the spherical case) of the minimisation problem proposed by Helfrich in 1973, modelling lipid bilayer membranes. On the way to prove the main res…
In this paper, we prove the long-time existence and uniqueness of the conical Kähler-Ricci flow with weak initial data which admits density for some on Fano manifold. Furthermore, we study the convergence behavior of this kind of flow.
This paper studies the Glosten Milgrom model whose risky asset value admits an arbitrary discrete distribution. Contrast to existing results on insider's models, the insider's optimal strategy in this model, if exists, is not of feedback type. Therefore a weak formulation of equilibrium is proposed. In this weak formul…
We study the quantization of coupled Kähler-Einstein (CKE) metrics, namely we approximate CKE metrics by means of the canonical Bergman metrics, so called the ``balanced metrics''. We prove the existence and weak convergence of balanced metrics for the negative first Chern class, while for the positive first Chern clas…
Unified approach to stochastic Volterra systems' deviations.
problem Large and moderate deviations for stochastic Volterra systems.
method Weak convergence approach by Budhijara, Dupuis and Ellis.
result Unified treatment of deviations for a broad class of stochastic Volterra equations.
Study on fourth order Lamm-Riviere system for biharmonic mappings in 4D.
problem Higher order regularity and sharp Holder continuity of weak solutions.
method Optimal higher order regularity and sharp Holder continuity through analysis of the Lamm-Riviere system.
result Derive weak compactness for sequences of weak solutions with uniformly bounded energy.
Paper proves large deviation principle for stochastic approximations.
problem Asymptotic estimates of learning algorithm deviations.
method Weak convergence approach to large deviations.
result Identifies appropriate scaling sequence and new representation for rate function.
Novel weak MLMC scheme for Lévy-driven SDEs, applied to financial derivatives pricing.
problem Approximating solutions to Lévy-driven SDEs for financial derivatives pricing.
method Weak multilevel Monte-Carlo scheme with state space discretization of Lévy processes.
result Efficient approximation of financial derivatives pricing models.
Paper investigates conditions for independence of weak gradients on metric spaces.
problem Dependence of weak gradients on in arbitrary metric measure spaces.
method Investigates the Bounded Interpolation Property to ensure independence of weak gradients.
result Bounded Interpolation Property guarantees independence of weak gradients.
New bounds for generative models under weaker assumptions.
problem Establishing convergence guarantees for generative models under weak assumptions.
method Non-asymptotic 2-Wasserstein distance bounds for probability flow ODEs under weak log-concavity and Lipschitz continuity.
result Concrete convergence rates for generative models, including non-log-concave distributions.
Simulating integrated Volterra square-root processes and Volterra Heston models via Inverse Gaussianq-fin.MF
A new simulation method for Volterra processes improves convergence for rough kernels.
problem Simulating Volterra processes with singular kernels.
method iVi (integrated Volterra implicit) scheme based on Inverse Gaussian distribution.
result The iVi scheme achieves weak convergence with few time steps, especially for rough kernels.
The significance of the study of the theoretical and practical properties of AdaBoost is unquestionable, given its simplicity, wide practical use, and effectiveness on real-world datasets. Here we present a few open problems regarding the behavior of "Optimal AdaBoost," a term coined by Rudin, Daubechies, and Schapire …
Cubature on Wiener space [Lyons, T.; Victoir, N.; Proc. R. Soc. Lond. A 8 January 2004 vol. 460 no. 2041 169-198] provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast…
Quantizes Willmore energy in Riemannian manifolds with bounded energy and area.
problem Quantization of Willmore energy in bounded energy and area conditions.
method Uniform boundedness of Willmore energy and area, weak convergence of maps, and conformal structures in compact domain.
result Quantization of Willmore energy holds under specified conditions.