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 ...

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 ...

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, ...

Studies mathematical theories and techniques for modeling financial markets. Specific topics include the binomial model, risk neutral pricing, stochastic calculus, connection to partial differential ...

Stochastic processes as a research area focuses on the mathematical modeling and analysis of systems that evolve randomly over time, typically formalized as families of random variables indexed by ...

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 ...

Randomness is inherent to real world problems so faculty research in this area includes the development and application of probabilistic tools to model, predict, and analyze randomness in applications ...