We start by showing that the finite-time absolute ruin probability in the classical risk model with constant interest force can be expressed in terms of the transition probability of a positive Ornstein-Uhlenbeck type process, say X. Our methodology applies to the case when the dynamics of the aggregate claims process …
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48 results for “finite-time transition density”
New method calibrates stochastic reduced-order models from data efficiently.
problem Challenges in estimating drift and diffusion coefficients from data for high-dimensional systems.
method Uses a novel relationship between conditional score and transition density to constrain model coefficients directly from finite-lag statistics.
result Validated on various systems, the method reproduces statistical and dynamical properties of the original models.
Proposes a method for approximating transition densities of SDEs driven by gamma processes.
problem Calculating transition densities for SDEs driven by gamma processes.
method Taylor-type approximation and conditional expectation of multiple stochastic integrals.
result Efficiency of the proposed method demonstrated through numerical tests.
Study refracted skew Brownian motion, find densities and asymptotics.
problem Modeling and analyzing refracted skew Brownian motion.
method Perturbation approach to find potential densities, transition density, and asymptotic behaviors.
result Expressions and asymptotic behaviors of refracted skew Brownian motion.
MAFLA improves sampling from heavy-tailed distributions using MH-inspired corrections.
problem Sampling from heavy-tailed and multimodal distributions when neither target nor proposal densities can be evaluated.
method Metropolis-Adjusted Fractional Langevin Algorithm (MAFLA) with Score Balance Matching.
result MAFLA significantly improves finite-time sampling accuracy over unadjusted fractional Langevin dynamics.
FourNet approximates financial transition densities using Fourier transforms.
problem Approximating transition densities in finance with high accuracy.
method FourNet is a novel FFNN with Gaussian activation, learning from characteristic functions.
result FourNet can approximate transition densities arbitrarily well with finite neurons.
Nonreversible Gauge Fields in Fokker--Planck Dynamics: Supersymmetric Hamiltonians and Learned Finite Forcescond-mat.dis-nn
New gauge fields modify Fokker-Planck dynamics without changing the stationary state.
problem Understanding and modifying nonreversible dynamics in Fokker-Planck models.
method Formulate nonreversible perturbations as gauge fields, mapping to supersymmetric Hamiltonians, and learning finite forces.
result Learned finite forces can recover the optimal Lyapunov-equation solution in nonconvex landscapes.
We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existen…
We prove a Weyl Law for the phase transition spectrum based on the techniques of Liokumovich-Marques-Neves. As an application we give phase transition adaptations of the proofs of the density and equidistribution of minimal hypersufaces for generic metrics by Irie-Marques-Neves and Marques-Neves-Song, respectively. We …
We present a plausible micro-founded model for the previously postulated power law finite time singular form of the crash hazard rate in the Johansen-Ledoit-Sornette model of rational expectation bubbles. The model is based on a percolation picture of the network of traders and the concept that clusters of connected tr…
New findings confirm parallels to De Giorgi's conjecture for phase transitions in higher dimensions.
problem Understanding phase transitions with bounded index in higher-dimensional spaces.
method Establishing parallels to De Giorgi's conjecture for general solutions of bounded Morse index.
result Finite index solutions to the Allen--Cahn equation in are one-dimensional, and this holds for all .
Persistent entropy detects phase transitions in complex systems.
problem Detecting phase transitions in complex systems.
method Established a general theorem for persistent entropy to reliably detect phase transitions, introduced operational framework for finite-time computations.
result Persistent entropy exhibits an asymptotically non-vanishing gap across phases, robust numerical signatures across experiments.
New models for short rates show longer periods at higher rates.
problem Modeling longer periods of higher interest rates.
method Developed a class of time-homogeneous one-factor Markov diffusion models with specific boundary conditions.
result Explicit expressions for bond prices and transition densities in new probability measure.
In this paper we introduce efficient Monte Carlo estimators for the valuation of high-dimensional derivatives and their sensitivities (''Greeks''). These estimators are based on an analytical, usually approximative representation of the underlying density. We study approximative densities obtained by the WKB method. Th…
Neural Galerkin Normalizing Flows for Bayesian Inference of Diffusions with Inaccessible Boundariescs.LG
New method learns diffusion transition density for Bayesian inference.
problem Bayesian inference on diffusions with inaccessible boundaries.
method Neural Galerkin framework to solve FP equation with Dirac mass.
result Approximates likelihood function for efficient posterior sampling.
We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Levy-type martingale subject to default. This class of models allows for local volatility, local default intensity, and a locally dependent Levy measure. Generalizing and extending the novel adjoint expansion technique o…
This paper derives the non-analytic solution to the Fokker-Planck equation of fractional Brownian motion using the method of Laplace transform. Sequentially, by considering the fundamental solution of the non-analytic solution, this paper obtains the transition probability density function of the random variable that i…
The paper tackles joint learning of linear systems, improving accuracy with pooled data.
problem Estimating transition matrices of multiple related linear systems more accurately.
method Developed novel techniques to bound estimation errors and establish high probability bounds for singular values.
result Significant gains in accuracy achieved by pooling data across systems.
We show that a surface group contained in a reductive real algebraic group can be deformed to become Zariski dense, unless its Zariski closure acts transitively on a Hermitian symmetric space of tube type. This is a kind of converse to a rigidity result of Burger, Iozzi and Wienhard.
The paper introduces new estimators for multivariate functions using Fourier methods.
problem Estimating multivariate functions like densities and regression functions.
method Monte Carlo estimators based on the Fourier integral theorem.
result Established rates of convergence for new estimators, often superior to existing methods.
We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the projection to the manifold of Brownian motions developed in the frame bundle lead …
The goal of reinforcement learning (RL) is to let an agent learn an optimal control policy in an unknown environment so that future expected rewards are maximized. The model-free RL approach directly learns the policy based on data samples. Although using many samples tends to improve the accuracy of policy learning, c…
Empirical Transfer Operators and Finite-Sample Change Detection for Noisy Expanding Interval Mapsstat.ML
Detect changes in noisy dynamical systems using empirical approximations and finite-sample bounds.
problem Change detection in noisy dynamical systems
method Partition-based empirical approximations and finite-state stationary distribution stability
result Finite-sample bound for empirical stationary density
We find various exact solutions for a new stochastic volatility (SV) model: the transition probability density, European-style option values, and (when it exists) the martingale defect. This may represent the first example of an SV model combining exact solutions, GBM-type volatility noise, and a stationary volatility …
New sampling method uses stochastic interpolants and FBSDEs.
problem Sampling from high-dimensional distributions with unnormalized densities.
method Stochastic interpolants and FBSDEs to define and solve diffusion process.
result Effective sampling from challenging distributions.
Fold maps associated to geodesic random walks on curved spaces.
problem Understanding the behavior of geodesic random walks on curved surfaces.
method Analyzing mappings from the unit tangent sphere to a manifold with non-positive curvature.
result For odd powers of the unit tangent sphere, these mappings are fold maps.
Study phase transitions in noisy transformer dynamics on spheres.
problem Understanding phase transitions in noisy transformer dynamics on spheres.
method Sharp Beckner--Onofri/logarithmic HLS inequality, Funk--Hecke/Bessel coefficients, degree-two quartic obstruction.
result Sharp global-minimizer dichotomy and phase transitions in noisy transformer dynamics in arbitrary dimension.
New study shows low-degree polynomial algorithms struggle at clause densities close to Fix's.
problem Finding satisfying assignments in random k-SAT formulas at high clause densities.
method Analysis of low-degree polynomial algorithms and a new many-way overlap gap property.
result No efficient algorithms can find satisfying assignments at clause densities close to Fix's.
Paper proposes a new approach to optimal transport for vector and matrix densities.
problem Optimal transport for vector and matrix densities with positivity and action transitivity constraints.
method Gauge-theoretic approach using semi-direct product groups of diffeomorphisms and gauge transformations.
result Bures-type metrics on semi-direct product groups relate to Wasserstein-type metrics on vector and matrix densities via Riemannian submersions.
Graph diffusion processes approximate manifold heat semigroups using graph transition matrices.
problem Approximating manifold heat semigroups from graph data under low regularity conditions.
method Iterating graph transition matrix to approximate , bounding error in -norm.
result Convergence rates for manifold heat semigroup approximation, valid for in-sample and out-of-sample.
Anosov flows found on many hyperbolic 3-manifolds.
problem Existence of Anosov flows on hyperbolic 3-manifolds.
method Explicit construction of Anosov flows on fibered hyperbolic 3-manifolds.
result Positive density of fibered hyperbolic manifolds carrying Anosov flows.
Study non-transitive pseudo-Anosov flows using group actions.
problem Characterize pseudo-Anosov flows in 3-manifolds.
method Extend pseudo-Anosov action to non-transitive flows, use group actions on orbit spaces and boundary at infinity.
result Pseudo-Anosov flows in 3-manifolds are determined by their group actions on boundary at infinity.
We study an extension of the classic stochastic multi-armed bandit problem which involves multiple plays and Markovian rewards in the rested bandits setting. In order to tackle this problem we consider an adaptive allocation rule which at each stage combines the information from the sample means of all the arms, with t…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a diffusion equation with a diffusion coefficient that inversely depends on the dat…
Stable solutions to a specific equation are one-dimensional.
problem Stability and dimensionality of solutions to the Allen-Cahn equation.
method Analysis of stable solutions with bounded energy density.
result Stable solutions to the Allen-Cahn equation are one-dimensional.
We study optimal estimation for sparse principal component analysis when the number of non-zero elements is small but on the same order as the dimension of the data. We employ approximate message passing (AMP) algorithm and its state evolution to analyze what is the information theoretically minimal mean-squared error …
This article is devoted to the maximisation of HARA utilities of L{é}vy switching process on finite time interval via dual method. We give the description of all f-divergence minimal martingale measures in initially enlarged filtration, the expression of their Radon-Nikodym densities involving Hellinger and Kulback-Lei…
This work explores efficient reinforcement learning with density features in low-rank MDPs.
problem Efficient reinforcement learning with density features in low-rank MDPs.
method Proposes algorithms for off-policy estimation and online construction of exploratory data distributions.
result Demonstrates sample-efficient learning with density features in low-rank MDPs, overcoming technical challenges.
In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a new dual-tree based variational approach for approximating the transition matrix…
The Sinkhorn-Knopp algorithm converges quickly but the number of iterations is poorly understood.
problem Understanding the number of iterations required for the Sinkhorn-Knopp algorithm to converge.
method Analyzing the Sinkhorn-Knopp algorithm for matrices with a specific density threshold.
result The Sinkhorn-Knopp algorithm requires iterations for matrices with density .
Phase Transition of Dynamical Herd Behaviors in Financial Marketscond-mat.stat-mech
We study the phase transition of dynamical herd behaviors for the yen-dollar exchange rate in the Japanese financial market. It is obtained that the probability distribution of returns satisfies the power-law behavior with three different values of the scaling exponent 3.11 (one time lag = 1 minute), 2.81 (30 minut…
Study learns linear system dynamics from noisy bilinear data.
problem Learning linear dynamics from bilinear observations with process and measurement noise.
method Regression with Kronecker product design, data-dependent and independent error bounds.
result Upper bounds on statistical error rates and sample complexity for learning dynamics matrices.
Determination of the critical points for systems of directed percolation class using machine learningcond-mat.stat-mech
Machine learning predicts critical points for directed percolation models.
problem Determining critical points for directed percolation models.
method Supervised and unsupervised machine learning algorithms (CNN and DBSCAN) were used.
result Machine learning accurately predicts critical points for both models.
This paper gives a brief overview on the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inferences of instantaneous returns and volatility functions of time-homogeneous and time-dependent diffusion processes, and estimation of transition densities and st…
Paper predicts in-situ metro passenger density using smart card data.
problem Crowd management in metro systems.
method Statistical models and EM algorithm for time-dependent OD matrix and travel time cost estimation.
result Accurate prediction of in-situ passenger density for future time points.
Generative Stochastic Networks (GSNs) have been recently introduced as an alternative to traditional probabilistic modeling: instead of parametrizing the data distribution directly, one parametrizes a transition operator for a Markov chain whose stationary distribution is an estimator of the data generating distributio…
We reprove a result concerning certain ruin in the classical problem of the probability of ruin with risky investments and several of it's generalisations. We also provide the combined transition density of the risk and investment processes in the diffusion case.
The paper approximates CARMA models for option pricing.
problem Approximating the transition density of CARMA(p, q) models.
method Using Gauss-Laguerre quadrature and time changed Brownian Motion.
result Provides an analytical formula for option prices.