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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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
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48 results for “functional weak convergence”
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.
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.
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.
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.
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.
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.
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…
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.
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.
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.
Topological Causal Effectsstat.ME
New method estimates causal effects in complex spaces using topological structures.
problem Challenges in estimating causal effects in non-Euclidean spaces.
method Developed a topological causal inference framework using power-weighted silhouette functions of persistence diagrams.
result Successfully quantifies topological treatment effects across various complex outcomes.
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 …
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…
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.
Paper presents a new policy gradient theorem using weak derivatives for reinforcement learning.
problem Continuous state-action reinforcement learning problems.
method Introduced an alternative policy gradient theorem using weak derivatives.
result The new approach yields algorithms that converge almost surely to stationary points of the value function.
We investigate a variety of stability properties of Haezendonck-Goovaerts premium principles on their natural domain, namely Orlicz spaces. We show that such principles always satisfy the Fatou property. This allows to establish a tractable dual representation without imposing any condition on the reference Orlicz func…
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.
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…
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.
Stein variational gradient descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate given distributions, based on an efficient gradient-based update that guarantees to optimally decrease the KL divergence within a function space. This paper develops the first th…
The paper studies deep neural networks with Gaussian weights and finds their asymptotic behavior.
problem Understanding the behavior of deep neural networks with large width.
method Function-space perspective, Gaussian process analysis, weak convergence in large-width limit.
result Deep neural networks with large width converge to a continuous Gaussian process.
The Mean Curvature Measuremath.AP
We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is weakly continuous with respect to almost everywhere convergence. We also establish a …
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…
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is an iterative scheme born from the adaptation of proximal point algorithm to nois…
The paper develops a deep neural network estimator for weakly dependent processes with various loss functions.
problem Learning weakly dependent processes with a broad class of loss functions.
method Sparse-penalized deep neural networks with -weak dependence structure and -coefficients.
result Oracle inequalities for the excess risk of the sparse-penalized deep neural networks estimators.
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.
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.
Extends stochastic modified equations for optimization algorithms.
problem Improving stochastic gradient optimization algorithms.
method Develops new stochastic modified equations (SMEs) for optimization.
result Computes linear error terms and proves convergence rates.
Unified treatment of CLTs for Lévy models across physics, finance, and econometrics.
problem Understanding convergence of stochastic integrals in Lévy models.
method Unified weak convergence results for Skorokhod spaces J1 and M1.
result General principles apply to specific settings, yielding new insights.
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.
Proposes a constrained labeling method for weakly supervised learning.
problem Combining weak supervision signals while navigating misleading correlations.
method Randomized constrained labeling within a defined space.
result Randomized constrained labeling converges after few iterations and outperforms other methods.
The stochastic gradient descent has been widely used for solving composite optimization problems in big data analyses. Many algorithms and convergence properties have been developed. The composite functions were convex primarily and gradually nonconvex composite functions have been adopted to obtain more desirable prop…
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.
Generative adversarial networks (GAN) approximate a target data distribution by jointly optimizing an objective function through a "two-player game" between a generator and a discriminator. Despite their empirical success, however, two very basic questions on how well they can approximate the target distribution remain…
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,…
In this paper we study integer multiplicity rectifiable currents carried by the subgradient (subdifferential) graphs of semi-convex functions on a -dimensional convex domain, and show a weak continuity theorem with respect to pointwise convergence for such currents. As an application, the -Hessian measures are ca…
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.
We show that K-energy minimizing movements agree with smooth solutions to Calabi flow as long as the latter exist. As corollaries we conclude that in a general Kahler class long time solutions of Calabi flow minimize both K-energy and Calabi energy. Lastly, by applying convergence results from the theory of minimizing …
Variational inference (VI) is a widely used framework in Bayesian estimation. For most of the non-Gaussian statistical models, it is infeasible to find an analytically tractable solution to estimate the posterior distributions of the parameters. Recently, an improved framework, namely the extended variational inference…
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.
Study of Kähler-Ricci flow on toric Fano varieties with preserved symplectic condition.
problem Analyzing the generalized Kähler-Ricci flow on toric Fano varieties.
method Establishing global existence, deriving entropy and energy functionals.
result Convergence of nonsingular solutions at infinity and weak convergence of the flow.
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.
This article analyzes the weak error of SGD optimization schemes.
problem Analyzing the error in SGD optimization schemes with respect to a test function.
method Weak error analysis for SGD type optimization schemes.
result The weak error decays at the same speed as in the strong sense.
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.