Results 281 to 290 of about 88,331 (317)

A Stochastic Integral Equation

SIAM Journal on Applied Mathematics, 1970
We investigate a stochastic integral equation of the form $x'(s) = y'(s) + \int_0^\alpha {K(s,t)dx(t)} $, where $y( s )$ is a process with orthogonal increments on the interval $T_\alpha = [0,\alpha ]$ and $K(s,t)$ is a continuous Fredholm or Volterra kernel on $T_\alpha \times T_\alpha $.
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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.
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Stochastic Equations Of Motion

2006
We have already observed that the full phase space description of a system of N particles (taking all 6N coordinates and velocities into account) requires the solution of the deterministic Newton (or Schrödinger) equations of motion, while the time evolution of a small subsystem is stochastic in nature.
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Stochastic Liouville Equations

Journal of Mathematical Physics, 1963
When a dynamical system has a perturbation which is considered as a stochastic process, the Liouville equation for the system in the phase space or the space of quantum-mechanical density operators is a sort of stochastic equation. The ensemble average of its formal integral defines the relaxation operator Φ(t) of the system.
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The approximation of the Boltzmann equation by stochastic equations

USSR Computational Mathematics and Mathematical Physics, 1988
See the review Zbl 0648.65082.
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On Stochastic Evolution Equations with Stochastic Boundary Conditions

Theory of Probability & Its Applications, 1994
Let \(I= (t_ 0, t_ 1)\) and \(G\) be a region in \(\mathbb{R}^ d\). The paper deals with a linear stochastic equation \[ d\xi_ t= A\xi_ t dt+ d\eta_ t, \qquad t\in I, \tag{*} \] where \(A\) is a symmetric elliptic differential operator of the form \(A= \sum_{| k|\leq 2p} a_ k \partial^ k\), \(d\eta\) is of the white noise type and the solution \(\xi ...
Albeverio, S., Rozanov, Yu. A.
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On solving stochastic differential equations

Monte Carlo Methods and Applications, 2019
Abstract This paper proposes a new approach to solving Ito stochastic differential equations. It is based on the well-known Monte Carlo methods for solving integral equations (Neumann–Ulam scheme, Markov chain Monte Carlo). The estimates of the solution for a wide class of equations do not have a bias, which distinguishes them from ...
Sergej M. Ermakov, Anna A. Pogosian
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The Backward Stochastic Liouville Equation

The Journal of Physical Chemistry B, 2004
The backward stochastic Liouville equation is formulated in a Dirac-type notation in order to emphasize the kinship with the backward diffusion equation and the Heisenberg picture of quantum mechanics. The backward equations are useful both for analytic treatments and for numerical methods since the solution contains the average value of the observable
Pedersen, Jørgen Boiden, Christensen, Michael   +1 more
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On stochastic Riccati equations for the stochastic LQR problem

Systems & Control Letters, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Positivity of the Stochastic Heat Equation

Potential Analysis, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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