Stratonovich representation helps analyze rank processes from semimartingales.
problem Analyzing rank processes from semimartingales with nondegenerate crossings.
method Using generalized Stratonovich integrals to represent rank processes.
result Decomposes relative log-return of market-weighted portfolios.
Study on stochastic flows on 7-dimensional spheres.
problem Stochastic processes on 7-dimensional spheres.
method Isometric stochastic flows of Stratonovich SDE on spheres.
result Properties of stochastic processes on Gromoll-Meyer exotic sphere.
Geometric integrals of Hölder continuous functions are defined over a 2D domain.
problem Defining integrals for Hölder continuous functions over a 2D domain.
method Summing discrete Stratonovich or Itô type terms over refining partitions.
result Two-dimensional extension of Young integral that coincides with recent integral.
New research connects evolutionary dynamics to Bayesian learning.
problem Connecting evolutionary biology and Bayesian learning.
method Rigorous mathematical proof using Kushner-Stratonovich equation and gradient flows.
result Discrete time filtering equations converge to Stratonovich interpretation of Kushner-Stratonovich equation.
The article constructs stochastic integration in Riemannian manifolds.
problem No specific problem stated; focuses on the construction of stochastic integration.
method Functional-analytic approach to stochastic integration in Riemannian manifolds.
result There are infinitely many stochastic integrals, and they are related by a simple formula.
Defines stochastic differential equations on manifolds using jets.
problem Defining stochastic differential equations on manifolds.
method Using 2-jets of smooth functions to interpret Itô SDEs numerically and geometrically.
result Geometric interpretation of Itô SDEs coefficients and their relationship to percentiles.
New method decomposes portfolio returns into generating and trading processes.
problem Decompose portfolio returns for arbitrary stock portfolios.
method Fisk-Stratonovich integration to extend decomposition to arbitrary portfolios.
result Portfolio returns can be represented by a structural process and trading process.
Options financial instruments designed to protect investors from the stock market randomness. In 1973, Fisher Black, Myron Scholes and Robert Merton proposed a very popular option pricing method using stochastic differential equations within the Ito interpretation. Herein, we derive the Black-Scholes equation for the o…
The paper approximates financial derivatives using neural networks and iterated integrals.
problem Approximating p-integrable financial derivatives. method Using iterated Stratonovich integrals and neural networks.
result Approximate solutions to the Lp-hedging problem. Extends nonlinear filtering to predictable jump times.
problem Filtering with jumps in both signal and observation, especially when jump times are known.
method Derive Kushner-Stratonovich and Zakai equations for predictable discontinuities.
result Extends classical nonlinear filtering results to a setting with predictable discontinuities.
The aim of these notes is to relate covariant stochastic integration in a vector bundle E (as in Norris \cite{Norris}) with the usual Stratonovich calculus via the connector $\K:TE \rightarrow E$ (cf. e.g. Paterson \cite{Paterson} or Poor \cite{Poor}) which carries the connection dependence.
The paper examines the consistency of Lasso regression applied to signature analysis of time series data.
problem Consistency of Lasso regression in signature analysis of time series data.
method The paper studies the consistency of Lasso regression applied to signature analysis of time series data, both theoretically and numerically.
result The Lasso regression is consistent both asymptotically and in finite sample for certain types of time series and processes.
STS clarifies chaos and stochastic dynamics, linking algebraic topology and physics.
problem Chaos and stochastic dynamics in arbitrary form SDEs.
method Supersymmetric theory of stochastic dynamics (STS) using generalized transfer operator (GTO) and topological field theories (TFT).
result Positive 'pressure' in GTOs corresponds to spontaneous breakdown of topological supersymmetry, explaining 1/f noise.
High order splitting schemes with complex timesteps are applied to Kolmogorov backward equations stemming from stochastic differential equations in Stratonovich form. In the setting of weighted spaces, the necessary analyticity of the split semigroups can be easily proved. A numerical example from interest rate theory,…
Develops optimal low-dimensional approximations to high-dimensional SDEs.
problem Approximating solutions to high-dimensional SDEs in a low-dimensional space.
method Introduces Ito-vector and Ito-jet projections for optimal approximation.
result Optimal projection filters yield better approximations than Stratonovich projection.
Revisits consumption-investment problem with anticipative noise.
problem Revisits classical consumption-investment problem with anticipative noise.
method Models risky-asset returns through a general α-integral, interpolating between Itô, Stratonovich, and related conventions.
result Derives closed-form optimal policies for logarithmic utility and constant volatilities in a market with n risky assets.
Develops optimal approximations for SDEs on submanifolds.
problem Approximating high-dimensional SDEs on lower-dimensional submanifolds.
method Ito-vector and Ito-jet projections based on differential geometry.
result Optimal approximations in mean-square sense for SDEs.
The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications in physics, but also in insurance, finance and economics. A definition is given for a class of stochastic integrals driven by a CTRW, that includes the Ito and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is…
We study harmonic and totally invariant measures in a foliated compact Riemannian manifold isometrically embedded in an Euclidean space. We introduce geometrical techniques for stochastic calculus in this space. In particular, using these techniques we can construct explicitely an Stratonovich equation for the foliated…
New algorithm samples from Ising models efficiently, even with outliers.
problem Sampling from Ising models with general interaction matrices.
method Combines MCMC and variational inference techniques.
result First polynomial time sampling algorithms for low-rank Ising models.
Study on stochastic flows on exotic spheres, exploring their properties.
problem Investigating stochastic processes on exotic (m+n+1)-dimensional spheres. method Constructing exotic manifolds from disjoint unions and identifying points using maps.
result Explicit homeomorphisms and stochastic processes on exotic spheres.
Study finds non-monotonic Value of Information in dynamic multi-market monopoly.
problem Investigates non-monotonicity in Value of Information for a price-setting monopolist.
method Uses a Bayesian inverse problem with Kalman-Bucy-Stratonovich filter in a dynamic discrete model.
result Non-monotonic relationship between signal variance and Value of Information.
Study on stochastic covariant derivatives in curved space-time.
problem Analyzing covariant derivatives in curved space-time under stochastic processes.
method Using Itô-Wiener processes and stochastic calculus, including Besov spaces, Schrödinger operators, and white noise.
result Developed a framework for stochastic geodesics and white noise in fractoid spaces.
Study rolling dynamics with random slipping and twisting using large deviation principles.
problem Analyzing the stability of a rolling model with random slipping and twisting.
method Modelled as a stochastic differential equation on the orthonormal frame bundle, examined via large deviations.
result Proved large deviation principles for projection curves and their horizontal lifts on the base manifold.
We study a stochastic equation modeling the lay-down of fibers in the production process of nonwovens. The equation can be formulated as some manifold-valued Stratonovich stochastic differential equation. Especially, we study the long time behaviour of the stochastic process. Demanding mathematical difficulties arising…
We reconsider the problem of calculating a general spectral correlation function containing an arbitrary number of products and ratios of characteristic polynomials for a N x N random matrix taken from the Gaussian Unitary Ensemble (GUE). Deviating from the standard "supersymmetry" approach, we integrate out Grassmann …
Develops trinomial models using cubature methods for financial derivative pricing.
problem Pricing financial derivatives in complex stochastic market models.
method Cubature methods applied to Wiener space for constructing trinomial models.
result Numerical solutions compare favorably with Black-Scholes model.
Unified geometric framework for Brownian motion on various manifolds.
problem Modeling Brownian motion on complex Riemannian manifolds.
method Constructing stochastic differential equations with noise and drift terms aligned with Laplace-Beltrami operators.
result Geometrically transparent and mathematically consistent foundation for diffusion processes.
Bayesian model predicts circular data with fast Gibbs sampling.
problem Predicting circular data in scientific fields.
method Expressive von Mises quasi-processes with Stratonovich augmentation for posterior inference.
result Fast Gibbs sampling for posterior inference.
The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.
problem Approximating functionals of non-geometric rough paths.
method Extending rough paths with time and quadratic variation terms, proving uniform approximation.
result Linear functionals of extended signatures uniformly approximate continuous functionals.
Study random walks on manifolds to understand geometric properties.
problem Understanding geometric properties of manifolds through random walks.
method Volume sampling random walks on Riemannian and sub-Riemannian manifolds.
result Passes from geodesics and volumes to diffusions and their generators.
This paper studies the question of filtering and maximizing terminal wealth from expected utility in a partially information stochastic volatility models. The special features is that the only information available to the investor is the one generated by the asset prices, and the unobservable processes will be modeled …
Paper corrects and expands stochastic Lie systems theory.
problem Stochastic Lie systems and their properties.
method Corrected stochastic Lie theorem, introduced new stochastic Lie systems.
result Stochastic Lie systems can differ significantly between Stratonovich and Itô approaches.
New integration method improves BSDE-based PDE solvers.
problem Discretization bias in standard BSDE-based solvers.
method Proposed Stratonovich-based BSDE formulation with stochastic Heun integration.
result Eliminates bias issues and outperforms EM-based variants.
In this article we develop geometric versions of the classical Langevin equation on regular submanifolds in euclidean space in an easy, natural way and combine them with a bunch of applications. The equations are formulated as Stratonovich stochastic differential equations on manifolds. The first version of the geometr…