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.
New algorithms for approximating stochastic processes efficiently.
problem Finding accurate finite approximations for stochastic processes.
method Develops new algorithms and fast implementations for approximating stochastic processes.
result Efficient approximations for stochastic processes can be found.
Large deviation principles for multivariate stochastic volatility models.
problem Understanding the behavior of log-processes in multivariate stochastic volatility models.
method Establishing a comprehensive sample path large deviation principle for log-processes.
result Asymptotic formulas for first exit times and barrier option prices derived from the LDP.
The paper generalizes the construction by stochastic flows of consistent utility processes introduced by M. Mrad and N. El Karoui in (2010). The utilities random fields are defined from a general class of processes denoted by $\GX$. Making minimal assumptions and convex constraints on test-processes, we construct by co…
Study approximates rough stochastic volatility models using diffusion processes.
problem High computational cost in simulating rough stochastic volatility models.
method Approximates stochastic Volterra equations with an N-dimensional diffusion process.
result Approximations converge strongly with superpolynomial rate in N.
BNP extends Neural Processes using bootstrap to better model uncertainty.
problem Limitation of NP in modeling stochastic processes with a single latent variable.
method Introduces BNP by incorporating bootstrap to estimate uncertainty without assuming a specific form.
result Demonstrates improved flexibility and robustness of BNP on various data types.
The mathematical model of a linear system with the short memory about own stochastic behavior is proposed. It is assumed that the system is under a continual influence of independent stochastic impulses. In a short memory approximation the expression of the stochastic process is found. An application of the model propo…
The sequence of moments of a vector-valued random variable can characterize its law. We study the analogous problem for path-valued random variables, that is stochastic processes, by using so-called robust signature moments. This allows us to derive a metric of maximum mean discrepancy type for laws of stochastic proce…
New method learns stochastic process representations without exact reconstruction.
problem Learning exact representations of high-dimensional noisy stochastic processes.
method CReSP framework for contrastive learning of stochastic processes.
result Effective for learning representations of various stochastic processes.
Incomplete financial markets are considered, defined by a multi-dimensional non-homogeneous diffusion process, being the direct sum of an Itô process (the price process), and another non-homogeneous diffusion process (the exogenous process, representing exogenous stochastic sources). The drift and the diffusion matrix …
Regularized SB process speeds up generative modeling.
problem Slow sampling and training times in SB-based models.
method Regularization terms to reduce timesteps and training time.
result Faster sampling speed for generative modeling.
New model improves field learning with improved equivariance.
problem Learning equivariant stochastic fields.
method Equivariant Gaussian processes and Steerable Conditional Neural Processes.
result SteerCNPs significantly improve performance in transfer learning tasks.
Neural Processes combine the strengths of neural networks and Gaussian processes to achieve both flexible learning and fast prediction in stochastic processes. However, a large class of problems comprises underlying temporal dependency structures in a sequence of stochastic processes that Neural Processes (NP) do not e…
This paper extends subordinated models to include stochastic time changes, improving financial modeling.
problem Improving financial models to better capture market features like jump clustering and volatility persistence.
method Subordinated processes with Levy and stochastic arrival mechanisms.
result Strong consistency and asymptotic normality results for VG and VGSA processes under various stochastic arrival models.
New learnability criteria for non-iid processes equivalent to online learning.
problem Statistical learning under non-iid stochastic processes is underdeveloped.
method Defined two learnability notions and showed their equivalence to online learning.
result Learnability criteria for non-iid processes are equivalent to online learning.
The paper shows robustness of Hilbert space-valued stochastic volatility models to perturbations.
problem Robustness of Hilbert space-valued stochastic volatility models to measurement or approximation errors.
method Quantifying the error induced by volatility perturbations and studying robustness of volatility process with finite dimensional approximations.
result Explicit bounds for the induced error in terms of approximation of the underlying parameter.
The paper introduces new KMEs to capture stochastic process filtrations.
problem Missing filtration information in stochastic processes.
method Higher order kernel mean embeddings (KMEs) conditioned on filtrations.
result Consistent estimators and tests for filtration-sensitive information.
Study stochastic processes on surfaces in contact sub-Riemannian manifolds using Riemannian approximations.
problem Analyzing stochastic processes on surfaces in contact sub-Riemannian manifolds.
method Employing Riemannian approximations, a second order partial differential operator is derived on the surface. The stochastic process moves along the characteristic foliation induced by the contact distribution.
result Elliptic characteristic points are inaccessible, while hyperbolic characteristic points are accessible from separatrices.
Solves optimal control for stochastic processes with absorbing states.
problem Optimal control of stochastic processes with absorbing states.
method Solves through system of partial differential equations.
result Explicit solution for Merton portfolio problem with default probability.
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate…
New model estimates higher-order interactions in stochastic processes using lower-dimensional projections.
problem Estimating higher-order interaction effects in stochastic processes with limited data.
method Additive Poisson Process (APP) combines information geometry and generalized additive models to model intensity functions in lower dimensions.
result The model can estimate higher-order intensity functions with sparse data.
LatentFlow simplifies conditioning of stochastic processes without training.
problem Intractable conditional laws for complex stochastic models.
method Writing stochastic process as latent innovation, reducing conditioning to latent-space inference.
result Exact conditional sampling across various model classes.
Unified reinforcement learning and stochastic processes with action-driven processes.
problem Combining reinforcement learning and stochastic processes for efficient control.
method Action-driven processes, leveraging control-as-inference, and minimizing Kullback-Leibler divergence.
result Action-driven processes unify reinforcement learning and stochastic processes, equivalent to maximum entropy reinforcement learning.
This work introduces a new model for complex stochastic processes.
problem Difficulties in representing non-stationary distributions with conventional models.
method Recurrent Autoregressive Flows using normalizing flows with recurrent neural connections.
result Demonstrates the effectiveness of the proposed model through experiments.
Scalable Gaussian process models trained with unbiased stochastic ELBO.
problem Training large capacity Gaussian process models on huge datasets.
method Unbiased stochastic variational inference for scalable GPs.
result Accurate inference on large datasets with up to 10 million basis functions.
Riemannian stochastic gradient descent approximates a diffusion process called Riemannian stochastic modified flow.
problem Improving convergence rate of Riemannian stochastic gradient descent.
method Using stochastic differential geometry, the paper shows RSGD can be approximated by the Riemannian stochastic modified flow (RSMF).
result RSGD can be approximated by the solution to the RSMF driven by an infinite-dimensional Wiener process, increasing the order of approximation.
New method for risk quantification using quantile processes and measure distortions.
problem Risk quantification and valuation in financial markets.
method Develops a novel stochastic valuation principle based on probability measure distortions induced by quantile processes.
result Introduces a system of subjective probability measures that indexes a stochastic valuation principle susceptible to probability measure distortions.
Proposes scale mixture of NNGPs for more flexible stochastic processes.
problem Limited focus on broadening the class of stochastic processes from NNGPs.
method Scale mixture of NNGPs with scale priors on last-layer parameters.
result Turns neural networks into a richer class of stochastic processes.
New neural processes use stacked Markov operators to improve flexibility.
problem Improving flexibility in neural processes.
method Stacking neural parameterized Markov transition operators in function space.
result MNPs outperform baseline models on various tasks.
The asymptotic pseudo-trajectory approach to stochastic approximation of Benaim, Hofbauer and Sorin is extended for asynchronous stochastic approximations with a set-valued mean field. The asynchronicity of the process is incorporated into the mean field to produce convergence results which remain similar to those of a…
This paper solves the inversion problem for jump processes using Markovian projections.
problem Calibrating jump-diffusion models with both local and stochastic features.
method Inverting Markovian projections for pure jump processes.
result Constructs calibrated local stochastic intensity (LSI) models for credit risk applications.
Extended CIR process with jumps at fixed dates for modeling overnight rates.
problem Modeling overnight rates with jumps at predetermined dates.
method Formal definition and existence proof of a CIR process with stochastic discontinuities.
result Extended CIR process inherits affine property and non-negativity.
Method uses deep learning to estimate traffic intensity.
problem Estimating stochastic intensity of traffic processes.
method Deep neural networks for nonlinear filtering.
result Deep learning method accurately estimates traffic intensity.
This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been motivated by a large and growing use of matrix-valued affine processes in finance, including multi-asset option pricing with stochastic volatil…
Stochastic gradient descent improves Gaussian process regression.
problem Efficiently solving large linear systems in Gaussian process regression.
method Developed a stochastic dual descent algorithm using insights from optimisation and kernel communities.
result Stochastic gradient descent is highly effective when done right.
The paper defines and analyzes set-valued stochastic integrals for Lévy processes.
problem Defining and analyzing set-valued stochastic integrals for Lévy processes.
method Extending classical definitions to convoluted integrals with square-integrable kernels, and proving properties of set-valued convoluted stochastic integrals.
result Set-valued convoluted stochastic integrals can be explosive and take extended vector values.
Paper proposes method for generating paths of stochastic volatility CGMY process for option pricing.
problem Generating accurate sample paths for stochastic volatility models for option pricing.
method Monte-Carlo method for European and American options, least square regression for calibration.
result Calibrated model parameters to S\&P 100 index options market using path-dependent options.
Stochastic models analyze traffic network performance.
problem Evaluate traffic system performance.
method Stochastic cell transmission models, preference functionals, Gaussian process regression.
result Illustrated in two case studies.
Stochastic flows of Stratonovich stochastic differential equations on exotic spheres have been studied. The consequences of the choice of exotic differential structure on stochastic processes taking place on the topological space Sm+n+1 as state space of the processes have been investigated. More precisely, we hav…
DSVNP uses global and local latent variables for improved neural process predictions.
problem Limited expressiveness of vanilla neural processes in capturing target-specific local variation.
method Introduces DSVNP combining global and local latent variables for prediction.
result Competitive prediction performance in multi-output regression and uncertainty estimation.
Overview of non-stochastic-gradient SA algorithms in signal processing and ML.
problem Dealing with large data sets and uncertainties in signal processing and machine learning.
method General framework of SA algorithms using Lyapunov functions.
result Unified convergence properties of non-stochastic-gradient algorithms.
Proposes logistic-beta process for modeling dependent probabilities with beta marginals.
problem Limited work on flexible and computationally convenient stochastic process extensions for dependent random probabilities.
method Introduces logistic-beta process with logistic transformation and beta marginals, capable of modeling dependence in discrete and continuous domains.
result Logistic-beta processes enable effective posterior inference and design of computationally tractable dependent Bayesian nonparametric models.
Method identifies regions of maximum dissimilarity in stochastic processes.
problem Comparing local characteristics of two random processes to find periods of maximum dissimilarity.
method Bayesian inference with integrated nested Laplace approximation for stochastic processes.
result Identifies regions of maximum dissimilarity with a certain volume.
Study BSΔE on lattices for asset price analysis.
problem Optimal investment and market equilibrium analysis in asset price models.
method Backward stochastic difference equations on lattices.
result Applications to optimal investment and market equilibrium analysis.
This study models target trajectories using stochastic processes for efficient tracking.
problem Efficiently modeling and predicting target trajectories in continuous time.
method Decomposes trajectory modeling into deterministic and stochastic components using Gaussian or Student's-t processes. result Demonstrates superior performance in tracking maneuvering targets compared to existing methods.
This paper applies AMP theory to improve learning tasks.
problem Improving learning efficiency by optimizing task-specific models.
method Uses aggregated Markov processes to reduce model complexity and enhance learning.
result Demonstrates how AMP theory can be effectively applied to stochastic learning.
Unified approach for data-driven control of stochastic processes.
problem Developing practical strategies for stochastic control problems with unknown dynamics.
method Reduction to rate-optimal estimators of invariant distribution risk.
result Data-driven strategies can achieve better performance than known methods.
This paper conditions non-linear infinite-dimensional diffusion processes.
problem Conditioning non-linear and infinite-dimensional diffusion processes.
method Infinite-dimensional Girsanov's theorem to condition function-valued stochastic processes.
result Conditioning of non-linear infinite-dimensional diffusion processes is achieved.