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Probabilistic methods for semilinear partial differential equations. Applications to finance

Dan Crisan, Konstantinos Manolarakis (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

With the pioneering work of [Pardoux and Peng, Syst. Contr. Lett.14 (1990) 55–61; Pardoux and Peng, Lecture Notes in Control and Information Sciences176 (1992) 200–217]. We have at our disposal stochastic processes which solve the so-called backward stochastic differential equations. These processes provide us with a Feynman-Kac representation for the solutions of a class of nonlinear partial differential equations (PDEs) which appear in many applications in the field of Mathematical Finance....

Probabilistic models for vortex filaments based on fractional brownian motion.

David Nualart, Carles Rovira, Samy Tindel (2001)

RACSAM

Se introduce una estructura de vorticidad basada en el movimiento browniano fraccionario con parámetro de Hurst H > 1/2 . El objeto de esta nota es presentar el siguiente resultado: Bajo una condición de integrabilidad adecuada sobre la medida ρ que controla la concentración de la vorticidad a lo largo de los filamentos, la energía cinética de la configuración está bien definida y tiene momentos de todos los órdenes.

Probabilistic models of vortex filaments

Franco Flandoli, Ida Minelli (2001)

Czechoslovak Mathematical Journal

A model of vortex filaments based on stochastic processes is presented. In contrast to previous models based on semimartingales, here processes with fractal properties between $1 / 2$ and $1$ are used, which include fractional Brownian motion and similar non-Gaussian examples. Stochastic integration for these processes is employed to give a meaning to the kinetic energy.

Probabilistische Metriken auf der Menge der nicht negativen Verteilungsfunktion.

Ulrich Höhle (1978)

Aequationes mathematicae

Probability against condition number and sampling of multivariate trigonometric random polynomials.

Böttcher, Albrecht, Potts, Daniel (2007)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Probability & incompressible Navier-Stokes equations: an overview of some recent developments.

Waymire, Edward C. (2005)

Probability Surveys [electronic only]

Probability and quantum symmetries. I. The theorem of Noether in Schrödinger's euclidean quantum mechanics

M. Thieullen, J. C. Zambrini (1997)

Annales de l'I.H.P. Physique théorique

Probability density for a hyperbolic SPDE with time dependent coefficients

Marta Sanz-Solé, Iván Torrecilla-Tarantino (2007)

ESAIM: Probability and Statistics

We prove the existence and smoothness of density for the solution of a hyperbolic SPDE with free term coefficients depending on time, under hypoelliptic non degeneracy conditions. The result extends those proved in Cattiaux and Mesnager, PTRF123 (2002) 453-483 to an infinite dimensional setting.