A backward stochastic differential equation (BSDE) is a stochastic differential equation with a terminal condition in which the solution is required to...

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution...

Deep backward stochastic differential equation method is a numerical method that combines deep learning with Backward stochastic differential equation (BSDE)...

Deep backward stochastic differential equation method is a numerical method that combines deep learning with Backward stochastic differential equation (BSDE)...

Deep backward stochastic differential equation method is a numerical method that combines deep learning with Backward stochastic differential equation (BSDE)...

for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their...

mechanics and information theory, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability...

specifically in the theory of Markovian stochastic processes in probability theory, the Chapman–Kolmogorov equation (CKE) is an identity relating the joint...

optimization problems, the analogous equation is a partial differential equation that is called the Hamilton–Jacobi–Bellman equation. In discrete time any multi-stage...

The Kolmogorov backward equation (KBE) and its adjoint, the Kolmogorov forward equation, are partial differential equations (PDE) that arise in the theory...

of assets—are stochastic. Backward stochastic differential equation Stochastic process Control theory Multiplier uncertainty Stochastic scheduling Separation...

about the process. The generator is used in evolution equations such as the Kolmogorov backward equation, which describes the evolution of statistics of the...

Feynman-Kac formula Fokker-Planck equation Kolmogorov backward equation Feller, W. (1949). "On the Theory of Stochastic Processes, with Particular Reference...

diffusion equations associated to these stochastic particles. It is best known for its derivation of the Schrödinger equation as the Kolmogorov equation for...

The most general continuous form of the replicator equation is given by the differential equation: x i ˙ = x i [ f i ( x ) − ϕ ( x ) ] , ϕ ( x ) = ∑ j...

Mark Kac, establishes a link between parabolic partial differential equations and stochastic processes. In 1947, when Kac and Feynman were both faculty...

runs. Asymptotic analysis Backward stochastic differential equation Calculus Copulas, including Gaussian Differential equations Expected value Ergodic theory...

unification of the theory of difference equations with that of differential equations, unifying integral and differential calculus with the calculus of finite...

values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation (or recurrence relation)...

proceeding backwards in time: This is the Bellman equation. DDP proceeds by iteratively performing a backward pass on the nominal trajectory to generate a...

Separation principle Sliding mode control State-transition matrix Stochastic differential equations Switching Kalman filter Lacey, Tony. "Chapter 11 Tutorial:...

Karoui, Nicole; Quenez, Marie-Claire; Peng, Shige (1997). "Backward Stochastic Differential Equations in Finance". Mathematical Finance. 7: 1–71. doi:10.1111/1467-9965...

_{t}\,dS_{t}+\psi _{t}\,dB_{t}\right)} . Backward stochastic differential equation Montin, Benoît. (2002) "Stochastic Processes Applied in Finance" [full citation...

estimated slope specified by function f on the right-hand side of the differential equation. k 1 {\displaystyle k_{1}} is the slope at the beginning of the...

specifically, in stochastic analysis – an Itô diffusion is a solution to a specific type of stochastic differential equation. That equation is similar to...

probabilistic models, noise conditioned score networks, and stochastic differential equations. They are typically trained using variational inference. The...

mathematician working in the field of Stochastic analysis, in particular Stochastic partial differential equations. He is currently Professor at Aix-Marseille...

difference method used for numerically solving the heat equation and similar partial differential equations. It is a second-order method in time. It is implicit...

Kolmogorov forward and backward equations. This is implemented as a python package Start with the integro-differential master equation ∂ p ( x , t ) ∂ t =...

a stochastic version of Pontryagin's maximum principle in control theory by introducing and studying the backward stochastic differential equations which...