Related papers: Calculo Estocastico, EDEs y EDPs
Infinite-dimensional stochastic differential equations (ISDEs) describing systems with an infinite number of particles are considered. Each particle undergoes a L\'evy process, and the interaction between particles is determined by the…
This thesis explores the historical progression and theoretical constructs of financial mathematics, with an in-depth exploration of Stochastic Calculus as showcased in the Binomial Asset Pricing Model and the Continuous-Time Models. A…
This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…
To study the nonlinear properties of complex natural phenomena, the evolution of the quantity of interest can be often represented by systems of coupled nonlinear stochastic differential equations (SDEs). These SDEs typically contain…
Considering stochastic partial differential equations of parabolic type with random coefficients in vector-valued H\"older spaces, we obtain a sharp Schauder estimate. As an application, the existence and uniqueness of solution to the…
This paper is concerned with the existence and uniqueness of weak solutions to the Cauchy-Dirichlet problem of backward stochastic partial differential equations (BSPDEs) with nonhomogeneous terms of quadratic growth in both the gradient of…
We consider a specific type of nonlinear partial differential equations (PDE) that appear in mathematical finance as the result of solving some optimization problems. We review some existing in the literature examples of such problems, and…
This paper is devoted to the study of the singularly perturbed second order partial integro-differential equations. The estimation of the solutions of Cauchy problem is obtained.
We consider long term average or `ergodic' optimal control poblems with a special structure: Control is exerted in all directions and the control costs are proportional to the square of the norm of the control field with respect to the…
In a preceding article, we have studied a generalization of the problem of finding a martingale on a manifold whose terminal value is known. This article completes the results obtained in the first article by providing uniqueness and…
We develop a stochastic calculus that makes it easy to capture a variety of predictable transformations of semimartingales such as changes of variables, stochastic integrals, and their compositions. The framework offers a unified treatment…
This paper deals with the existence of solutions for an elliptic system of partial differential equations. The solution method is based on the sub- and super-solutions approach. An application to a stochastic control problem is presented.…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
This paper explores the relationship between non-Markovian fully coupled forward-backward stochastic systems and path-dependent PDEs. The definition of classical solution for the path-dependent PDE is given within the framework of…
This paper presents a partial state of the art about the topic of representation of generalized Fokker-Planck Partial Differential Equations (PDEs) by solutions of McKean Feynman-Kac Equations (MFKEs) that generalize the notion of McKean…
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…
We study the minimization of the expected costs under stochastic constraint at the terminal time. The first and the main result says that for a power type of costs, the value function is the minimal positive solution of a second order…
The classical Feynman-Kac formula states the connection between linear parabolic partial differential equations (PDEs), like the heat equation, and expectation of stochastic processes driven by Brownian motion. It gives then a method for…
In this paper, we consider the Cauchy problem of semi-linear degenerate backward stochastic partial differential equations (BSPDEs in short) under general settings without technical assumptions on the coefficients. For the solution of…