Stochastic differential equations (SDEs) and random processes form a central framework for modelling systems influenced by inherent uncertainties. These mathematical constructs are used to rigorously ...

The study of stochastic differential equations (SDEs) has long been a cornerstone in the modelling of complex systems affected by randomness. In recent years, the extension to G-Brownian motion has ...

SIAM Journal on Numerical Analysis, Vol. 49, No. 5/6 (2011), pp. 2017-2038 (22 pages) General autonomous stochastic differential equations (SDEs) driven by one-dimensional Brownian motion in the ...

A mathematical statistical model is needed to obtain an option prime and create a hedging strategy. With formulas derived from stochastic differential equations, the primes for US Dollar/Chilean Pesos ...

(Conditional) generative adversarial networks (GANs) have had great success in recent years, due to their ability to approximate (conditional) distributions over extremely high-dimensional spaces.

This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic ...

Brownian motion and Langevin's equation. Ito and Stratonovich Stochastic integrals. Stochastic calculus and Ito's formula. SDEs and PDEs of Kolmogorov. Fokker-Planck, and Dynkin. Boundary conditions, ...

This book provides a lively and accessible introduction to the numerical solution of stochastic differential equations with the aim of making this subject available to the widest possible readership.

This paper is concerned with the long-time behavior of solutions for a class of stochastic semilinear degenerate equations with memory driven by nonlinear noise on ℝ n ...

This course is compulsory on the BSc in Actuarial Science. This course is available on the BSc in Business Mathematics and Statistics, BSc in Financial Mathematics and Statistics, BSc in Mathematics ...