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...

Stochastic partial differential equations (SPDEs) generalize partial differential equations via random force terms and coefficients, in the same way ordinary...

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

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions...

partial differential equations (PDEs) which may be with respect to more than one independent variable, and, less commonly, in contrast with stochastic differential...

In mathematics, stochastic analysis on manifolds or stochastic differential geometry is the study of stochastic analysis over smooth manifolds. It is...

mathematics, the Kardar–Parisi–Zhang (KPZ) equation is a non-linear stochastic partial differential equation, introduced by Mehran Kardar, Giorgio Parisi...

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

convection–diffusion equation is a parabolic partial differential equation that combines the diffusion and convection (advection) equations. It describes physical...

Kakutani makes between stochastic differential equations and the Itō process is effectively the same as Kolmogorov's forward equation, made in 1931, which...

adjoint of the infinitesimal generator of the underlying stochastic process. The Klein–Kramers equation is a special case of that. For a Feller process ( X...

In physics, a Langevin equation (named after Paul Langevin) is a stochastic differential equation describing how a system evolves when subjected to a combination...

In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives...

Tsirelson's stochastic differential equation (also Tsirelson's drift or Tsirelson's equation) is a stochastic differential equation which has a weak solution...

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

can be generalized to stochastic systems, in which case the HJB equation is a second-order elliptic partial differential equation. A major drawback, however...

with drift. It is an important example of stochastic processes satisfying a stochastic differential equation (SDE); in particular, it is used in mathematical...

of a stochastic differential equation (SDE). It is an extension of the Euler method for ordinary differential equations to stochastic differential equations...

while accounting for omitted degrees of freedom by the use of stochastic differential equations. Langevin dynamics simulations are a kind of Monte Carlo simulation...

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

stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance and stochastic differential equations...

the solution of a stochastic differential equation; Hörmander's original proof was based on the theory of partial differential equations. The calculus has...

differential equation Cauchy–Euler equation Riccati equation Hill differential equation Gauss–Codazzi equations Chandrasekhar's white dwarf equation Lane-Emden...

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

intersection of dynamical systems theory, statistical physics, stochastic differential equations (SDE), topological field theories, and the theory of pseudo-Hermitian...

particular, the theory of stochastic processes. He invented the concept of stochastic integral and stochastic differential equation, and is known as the founder...

stochastic differential equations (QSDE) that are analogous to classical Langevin equations. For the remainder of this article stochastic calculus will...

multifractals in turbulence, the stochastic differential equation for growth models for random aggregation (the Kardar–Parisi–Zhang equation) and his groundbreaking...

-martingale. The above leads to the alternate representation of the stochastic differential equation d X ( t ) = μ ( t ) d t + σ ( t ) d B ( t ) {\displaystyle...

the equation. If x is restricted to be an integer, a difference equation is the same as a recurrence relation A stochastic differential equation is a...