Results 301 to 310 of about 836,551 (359)

Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation.

Physical review. A, General physics, 1985
We develop a formulation of quantum damping theory in which the explicit nature of inputs from a heat bath, and of outputs into it, is taken into account.
C. Gardiner, M. Collett
semanticscholar   +1 more source

Stochastic Differential Equations [PDF]

, 1988
We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of ...
Steven E. Shreve, Ioannis Karatzas
openaire   +1 more source

Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations

Communications in Mathematics and Statistics, 2017
We study a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, which is based on an analogy between the BSDE and reinforcement learning with the gradient of ...
Weinan E, Jiequn Han, Arnulf Jentzen
semanticscholar   +1 more source

An Open-Loop Stackelberg Strategy for the Linear Quadratic Mean-Field Stochastic Differential Game

IEEE Transactions on Automatic Control, 2019
This paper is concerned with the open-loop linear–quadratic (LQ) Stackelberg game of the mean-field stochastic systems in finite horizon. By means of two generalized differential Riccati equations, the follower first solves a mean-field stochastic LQ ...
Yaning Lin, Xiushan Jiang, Weihai Zhang
semanticscholar   +1 more source

Stochastic Differential Equations

2009
The chapter begins with Section 4.1 in which motivational examples of random walks and stochastic phenomena in nature are presented. In Section 4.2 the concept of random processes is introduced in a more precise way. In Section 4.3 the concept of a Gaussian and Markov random process is developed. In Section 4.4 the important special case of white noise
Alexander Kukush, Andrey Pilipenko, Dmytro Gusak, Alexey Kulik, Yuliya Mishura   +4 more
  +7 more sources

Stochastic differential equations

Physics Reports, 1976
Abstract In chapter I stochastic differential equations are defined and classified, and their occurrence in physics is reviewed. In chapter II it is shown for linear equation show a differential equation for the averaged solution is obtained by expanding in ατ c , where α measures the size of the fluctuations and τ c their autocorrelation time. This
openaire   +3 more sources

Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications

, 2011
We give a survey of the developments in the theory of Backward Stochastic Differential Equations during the last 20 years, including the solutions’ existence and uniqueness, comparison theorem, nonlinear Feynman-Kac formula, g-expectation and many other ...
S. Peng
semanticscholar   +1 more source

Stochastic Differential Equations

1991
In previous chapters stochastic differential equations have been mentioned several times in an informal manner. For instance, if M is a continuous local martingale, its exponential e(M) satisfies the equality $$\mathcal{E}{(M)_t} = 1 + \int_0^t {\mathcal{E}{{(M)}_s}} d{M_s};$$ this can be stated: e(M) is a solution to the stochastic differential
Daniel Revuz, Marc Yor
openaire   +2 more sources

Stochastic Differential Equations

2019
In this chapter, we consider the stochastic differential equations and backward stochastic differential equations driven by G-Brownian motion. The conditions and proofs of existence and uniqueness of a stochastic differential equation is similar to the classical situation.
Radek Erban, S. Jonathan Chapman
  +6 more sources

Stochastic differential equations

2011
In this chapter we present some basic results on stochastic differential equations, hereafter shortened to SDEs, and we examine the connection to the theory of parabolic partial differential equations.
openaire   +4 more sources