You can calculate a derivative of densities for stochastic processes in some generalised sense which I do not at present understand, and do the normal calculus thing you do with a derivative. Stochastic differential equations arise, presumably ones in some sense involving this generalised derivative, can then solve some kind of problems for you. Or something.
Clearly this is a placeholder for a topic I do not have time for right now. 🏗
Bell, Denis R. 2006. The Malliavin Calculus. Courier Corporation. http://books.google.com?id=IVm8AQAAQBAJ.
Bichteler, Klaus, Jean-Bernard Gravereaux, and Jean Jacod. 1987. Malliavin Calculus for Processes with Jumps. Stochastics Monographs, v. 2. New York: Gordon and Breach Science Publishers.
Di Nunno, Giulia, B. K. Øksendal, and Frank Proske. 2009. Malliavin Calculus for Lévy Processes with Applications to Finance. Universitext. Berlin ; New York: Springer.
Friz, Peter K. 2005. “An Introduction to Malliavin Calculus.” Courant Institute of Mathematical Sciences.
Levajkovic, Tijana, and Dora Selesi. 2011. “Chaos Expansion Methods for Stochastic Differential Equations Involving the Malliavin Derivative, Part I.” Publications de L’Institut Mathematique 90 (104): 65–84. https://doi.org/10.2298/PIM1104065L.
Nualart, David. 2006. The Malliavin Calculus and Related Topics. 2nd ed. Probability and Its Applications. Berlin ; New York: Springer.
Osswald, Horst. 2012. Malliavin Calculus for Lévy Processes and Infinite-Dimensional Brownian Motion: An Introduction. Cambridge Tracts in Mathematics 191. Cambridge: Cambridge University Press.
Schiller, Eric Alexander. 2009. “Malliavin Calculus for Monte Carlo Simulation with Financial Applications.”
Zhang, Han. 2004. “The Malliavin Calculus.”