This paper provides an existence-and-uniqueness theorem characterizing the stochastic integral with respect to a Wiener process. The integral is represented as a mapping from the space of measurable and adapted pathwise locally integrable processes to the space of continuous adapted processes. It is characterized in te…
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48 results for “integrated process”
Counterexample shows Ito integrand needn't be locally square integrable.
problem Ito integrand's square integrability condition is not always met.
method Provided a counterexample to Ito's Lemma's integrability condition.
result Ito integrand needn't be locally square integrable.
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.
A new model DKMPP integrates covariates and uses an integration-free method for spatio-temporal point processes.
problem Training intractable deep spatio-temporal point processes with multimodal covariates.
method DKMPP uses a deep kernel to model complex relationships and an integration-free score matching method.
result DKMPP and score-based estimators outperform baseline models in spatio-temporal point processes.
A new adaptive binarization technique using fuzzy integrals improves image quality.
problem Improving image thresholding quality.
method FLAT (Fuzzy Local Adaptive Thresholding) based on fuzzy integrals.
result The proposed FLAT method produces better image quality than traditional algorithms and neural networks.
A new method simulates square-root processes efficiently.
problem Simulating square-root processes accurately and efficiently.
method Simulate the integrated square-root process instead of the square-root process itself.
result High precision with low number of time steps, and exact limiting Inverse Gaussian distributions.
A novel method for efficiently integrating spatiotemporal point processes.
problem Challenges in integrating spatiotemporal neural point processes, especially for flexible intensity functions.
method AutoSTPP (Automatic Integration for Spatiotemporal Neural Point Processes) extends a dual network approach to 3D STPP using ProdNet for decomposable parametrization of the integral network.
result AutoSTPP effectively sidesteps computational complexities and shows significant advantage in recovering complex intensity functions.
The paper evaluates integrals for fBm with various Hurst indices.
problem Evaluating integrals for stochastic processes with fractional Brownian motion for different Hurst indices.
method Analytic continuation from complex analysis to extend integral domain.
result Integral formulas for fBm with Hurst indices are derived.
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.
Study optimal control of diffusion processes with infimum or supremum costs.
problem Optimizing control of a diffusion process with costs dependent on its infimum or supremum.
method Introduced novel integral operators to solve two-dimensional singular control problems.
result Explicit solutions for optimal dividend problem with time-dependent preferences.
Efficient evaluation of joint pdf of a Lévy process, its extremum, and hitting time of the extremummath.PR
Derives integral representations for a Lévy process and its extremum, hitting time, with fast evaluation.
problem Efficiently evaluating the joint probability density function of a Lévy process, its supremum, and hitting time.
method Integral representations, Laplace-Fourier transforms, summation by parts, conformal deformation, trapezoid rules, Gaver-Wynn-Rho algorithm.
result Explicit calculations and fast evaluation of the joint cpdf for Lévy processes.
The aim of this article is to design a moment transformation for Student- t distributed random variables, which is able to account for the error in the numerically computed mean. We employ Student-t process quadrature, an instance of Bayesian quadrature, which allows us to treat the integral itself as a random variable…
New corrugation process solves -isometric maps with conical singularities.
problem Constructing -isometric maps from maps with conical singularities.
method Using the corrugation process to solve differential problems of Kuiper type.
result Proved that -isometric maps in codimension 1 are of Kuiper type.
Dirac Processes and Default Riskq-fin.PR
We introduce Dirac processes, using Dirac delta functions, for short-rate-type pricing of financial derivatives. Dirac processes add spikes to the existing building blocks of diffusions and jumps. Dirac processes are Generalized Processes, which have not been used directly before because the dollar value of non-Real nu…
The paper integrates multiple Gaussian process predictions using Monte Carlo sampling.
problem Accurate prediction of variables using multiple models.
method Log-linear pooling of Gaussian process predictions, combined with Monte Carlo sampling.
result The log-linear pooling method improves prediction accuracy compared to linear pooling.
New method integrates computer models from different disciplines with better predictive performance.
problem Integration of multi-disciplinary computer models with distinct complexities and computation times.
method Developed a linked deep Gaussian process (DGP) method that integrates individual Gaussian process emulators in a network.
result Linked deep Gaussian process emulators outperform standard LGP emulators and single DGPs fitted to the network as a whole.
NeuralChaos efficiently approximates complex stochastic processes.
problem Representing and computing square-integrable predictable processes over time.
method Introduces NeuralChaos, a neural operator architecture for -valued predictable processes.
result NeuralChaos achieves best -term chaoslet approximation rates and is dense in .
P3LS preserves privacy while integrating data across companies.
problem Privacy concerns in cross-organizational data exchange and integration.
method Privacy-preserving federated learning technique using SVD-based PLS and random masks.
result Improves prediction performance on process-related indicators.
DGPFM uses deep Gaussian processes to map functions accurately and quantify uncertainty.
problem Learning mappings between functional spaces, especially when data are noisy, sparse, or irregularly sampled.
method Constructs a sequence of GP-based linear and nonlinear transformations directly in function space, leveraging kernel integral transforms, GP conditional means, and nonlinear activations sampled from Gaussian processes.
result Empirical results show DGPFM outperforms existing methods in predictive accuracy and uncertainty calibration.
We replace the usual Convex Integration formula by a Corrugation Process and introduce the notion of Kuiper differential relations. This notion provides a natural framework for the construction of solutions with self-similarity properties. We consider the case of the totally real relation, we prove that it is Kuiper an…
We analyze exponential integrability properties of the Cox-Ingersoll-Ross (CIR) process and its Euler discretizations with various types of truncation and reflection at 0. These properties play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a class of sto…
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.
Study forward investment performance in semimartingale markets with stochastic factors.
problem Investigate forward investment performance in incomplete semimartingale markets with power risk preferences and stochastic integrated factors.
method Develop necessary and sufficient conditions for FIPP existence, use integral representations, and solve ill-posed HJB equations.
result Explicit constructions for time-monotone FIPPs in semimartingale models, generalizing from Brownian to semimartingale markets.
Bayesian approach for inhomogeneous Poisson process intensity estimation.
problem Intractable integral in likelihood of Gaussian Cox process.
method Joint modeling of intensity and cumulative intensity as transformed Gaussian process; exact MCMC sampler.
result Exact posterior inference without approximations.
For every adapted, càglàd process (strategy) and typical càdlàg price paths whose jumps satisfy some mild growth condition we define integral as a limit of simple integrals.
This paper examines the integration process of the Japanese major rice markets (Tokyo and Osaka) from 1881 to 1932. Using a non-Bayesian time-varying vector error correction model, we argue that the process strongly depended on the government's policy on the network system of the telegram and telephone; rice traders wi…
Novel Hilbert space Gaussian process improves sequential design accuracy and efficiency.
problem Efficiently implementing Gaussian process acquisition functions for expensive simulations.
method Proposed a truncated eigenbasis representation for closed-form evaluation of IMSE acquisition function.
result Significantly lower prediction error and reduced computation time compared to benchmarks.
Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation. We will assume that we can sample from the distribution of the process from time…
Novel method uses Gaussian process to estimate particle sizes from scattering data.
problem Estimating particle size distributions from noisy optical scattering measurements.
method Constrained Gaussian process regression with normalization constraints.
result Accurately reconstructs particle size distributions from noisy data.
DisCoveR efficiently discovers declarative process models from event logs.
problem Mining declarative process models from event logs efficiently and accurately.
method DisCoveR precisely formalizes an algorithm, uses a bit vector implementation, and rigorously evaluates performance.
result DisCoveR outperforms other declarative miners in accuracy and runtime.
The study characterizes straight-line flows in dynamic measure transport.
problem Tackles the challenge of designing flows that are easy to integrate.
method Characterizes straight-line flows using a PDE and Reynolds tensor.
result Characterizes affine-in-time interpolants and necessary conditions for flow geometry.
We propose a representation of Gaussian processes (GPs) based on powers of the integral operator defined by a kernel function, we call these stochastic processes integral Gaussian processes (IGPs). Sample paths from IGPs are functions contained within the reproducing kernel Hilbert space (RKHS) defined by the kernel fu…
Path Integral Method for Proportional Step and Proportional Double-Barrier Step Option Pricingq-fin.PR
Path integral method calculates barrier option prices.
problem Barrier option pricing in finance.
method Path integral method applied to trapezoid and square potential barriers.
result Analytical expressions for option pricing derived.
Motivated by applications to insurance mathematics, we prove some heavy-traffic limit theorems for process which encompass the fractionally integrated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution.
Paper develops methods for solving complex stochastic equations using Malliavin calculus.
problem Existence, uniqueness, and regularity of solutions to BSVIEs.
method Malliavin calculus for tackling diagonal processes and nonlinear dependence.
result Developed well-posedness results for BSVIEs, including probabilistic interpretation of PDEs and portfolio optimization.
Are Stock Markets Integrated? Evidence from a Partially Segmented ICAPM with Asymmetric Effectsq-fin.ST
In this paper, we test a partially segmented ICAPM for two developed markets, two emerging markets and World market, using an asymmetric extension of the multivariate GARCH process of De Santis and Gerard (1997,1998). We find that this asymmetric process provides a significantly better fit of the data than a standard s…
Researchers find the optimal exercise time for American options using a specific type of diffusion process.
problem Finding the optimal time to exercise American options with a time-dependent Ornstein-Uhlenbeck process.
method Optimal stopping problem, probabilistic arguments, non-linear Volterra-type integral equation, Picard iteration algorithm.
result They derive a non-linear Volterra-type integral equation and prove the exercise boundary's Lipschitz continuity and differentiability almost everywhere.
New method samples from time-integrated stochastic bridges using neural networks.
problem Sampling from time-integrated stochastic bridges with high accuracy and speed.
method Polynomial chaos expansion and artificial neural networks.
result Robust, data-driven Monte Carlo sampling with thousands of samples in milliseconds.
This paper extends explainability methods to non-Gaussian Gaussian Processes.
problem Making non-Gaussian GP models transparent and explainable.
method Proposes Integrated Gradient-based explainability for non-Gaussian GP models.
result Offers both analytical and approximate solutions for non-Gaussian GP models.
Study analyzes Lévy process structure on manifolds with conjugate points.
problem Microlocal analysis of Lévy processes on manifolds with conjugate points.
method Microlocal analysis, pseudodifferential operators, Fourier integral operators.
result Generator can be expressed as sum of pseudodifferential and Fourier integral operators.
This paper deals with the evaluation of double line integrals of the squared exponential covariance function. We propose a new approach in which the double integral is reduced to a single integral using the error function. This single integral is then computed with efficiently implemented numerical techniques. The perf…
A new framework for recycling Gaussian process approximations.
problem Efficiently combining multiple Gaussian process approximations.
method Construct variational ensembles using a dictionary of fitted Gaussian processes.
result Framework allows for various tasks and scalability.
We price European and American exchange options where the underlying asset prices are modelled using a Merton (1976) jump-diffusion with a common Heston (1993) stochastic volatility process. Pricing is performed under an equivalent martingale measure obtained by setting the second asset yield process as the numeraire a…
An online framework improves investment management by making incremental updates.
problem Offline investment processes restrict silos from collectively pursuing a unified goal.
method Developed an online algorithm workflow for portfolio management.
result The online framework outperforms market benchmarks and reduces overfitting.
By the classical Martingale Representation Theorem, replication of random vectors can be achieved via stochastic integrals or solutions of stochastic differential equations. We introduce a new approach to replication of random vectors via adapted differentiable processes generated by a controlled ordinary differential …
Integrates Fourier features for faster Gaussian process regression.
problem Efficiently scaling Gaussian process regression to large datasets.
method Integrated Fourier features for Gaussian processes.
result Improves Gaussian process regression speed to for a broad class of kernels.
Bayesian quadrature uses probabilistic models for estimating intractable integrals.
problem Estimating intractable integrals in complex models.
method Probabilistic, model-based approach using Gaussian processes.
result Comprehensive review and systematic taxonomy of Bayesian quadrature methods.
In the process of calculating Noether's conservation laws, two sets of integration by parts are performed. Here it is shown why the boundary terms from the first set of integration by parts vanish.