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Modeling bundle-valued forms on the path space with a curved iterated integral
The usual iterated integral map given by Chen produces an equivalence between the two-sided bar complex on differential forms and the de Rham complex...
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ON THE MAXIMUM PRINCIPLE FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH A PATH-WISE COST FUNCTIONAL
The maximum principle with a path-wise cost functional is constructed for one-dimensional stochastic differential equations with a symmetric integral...
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A càdlàg rough path foundation for robust finance
Using rough path theory, we provide a pathwise foundation for stochastic Itô integration which covers most commonly applied trading strategies and...
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Survey on Path-Dependent PDEs
In this paper, the authors provide a brief introduction of the path-dependent partial di.erential equations (PDEs for short) in the space of...
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Generalized integral Jensen inequality
In this paper we introduce necessary and sufficient conditions for a real-valued function to be preinvex. Some properties of preinvex functions and...
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Solving the chemical master equation for monomolecular reaction systems and beyond: a Doi-Peliti path integral view
The chemical master equation (CME) is a fundamental description of interacting molecules commonly used to model chemical kinetics and noisy gene...
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Rough Differential Equations Containing Path-Dependent Bounded Variation Terms
We consider rough differential equations whose coefficients contain path-dependent bounded variation terms and prove the existence and a priori...
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The Stochastic Integral
In this chapter, Itô’s stochastic integral and some of its basic properties are carefully introduced. The essential role of martingale theory is made...
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Integral Representations and Integral Identities
Working in the complex plane, in §1.1 we prove versions of the classical Cauchy-Pompeiu integral representation formula, Morera’s Theorem, the...
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Integral Equations: An Introduction
The theory of Integral Equations constitute an important topic in Mathematics as this is one of the most useful mathematical tools in both pure and...
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Surrender and Path-Dependent Guarantees in Variable Annuities: Integral Equation Solutions and Benchmark Methods
We investigate the evaluation problem of variable annuities by considering guaranteed minimum maturity benefits with constant or path-dependent...
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Stability of the minimum energy path
The minimum energy path (MEP) is the most probable transition path that connects two equilibrium states of a potential energy landscape. It has been...
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Approximating Maximum Integral Multiflows on Bounded Genus Graphs
We devise the first constant-factor approximation algorithm for finding an integral multi-commodity flow of maximum total value for instances where...
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Distribution-Path Dependent Nonlinear SPDEs with Application to Stochastic Transport Type Equations
By using a regularity approximation argument, the global existence and uniqueness are derived for a class of nonlinear SPDEs depending on both the...
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Multi-dimensional Path-dependent Forward-backward Stochastic Variational Inequalities
In this article, we consider a system of stochastic variational inequalities (SVIs) in the differential form. The system has a d -dimensional forward...
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Novel Stochastic Method for Multidimensional Fredholm Integral Equations
Integral equations have broad applications in various fields, such as applied mathematics, physics, engineering, geophysics, electricity and...
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Path Integrals
Integration of generalised 1-forms. The length of a path. Vector fields; conservative and symmetric vector fields.
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Finding a Shortest Non-Zero Path in Group-Labeled Graphs
We study a constrained shortest path problem in group-labeled graphs with nonnegative edge length, called the shortest non-zero path problem. ...
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The Integral
The idea of “integration” is as old as mathematics: it starts with the necessity of measuring areas delimited by curves. The problem is that our...