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 ...
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 ...
Backward Stochastic Differential Equations (BSDEs) constitute a class of stochastic processes where the solution is determined by a prescribed terminal condition rather than an initial one. These ...
The main aim of this paper is to develop some basic theories of neutral stochastic functional differential equations (NSFDEs). Firstly, we establish a local existenceuniqueness theorem under the local ...
A new algorithm developed by Naoki Masuda, with co-athors Kazuyuki Aihara and Neil G. MacLaren, can identify the most predictive data points that a tipping point is near. Published in Nature ...
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 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 ...
Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...
In this paper we examine the capacity of arbitrage-free neural stochastic differential equation market models to produce realistic scenarios for the joint dynamics of multiple European options on a ...
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