Results 261 to 270 of about 41,517 (308)

Nondemolition Continuous Measurement and the Quantum Stochastic Differential Equations

, 1998
Toshihico Arimitsu, Yukio Endo
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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 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
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ON STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

Mathematics of the USSR-Sbornik, 1975
In this paper we consider the Cauchy problem for second-order stochastic partial differential equations of parabolic type. We study linear and nonlinear equations for filtering Markov diffusion processes. Theorems on the existence, uniqueness and smoothness of solutions are proved.Bibliography: 21 items.
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Stochastic Differential Equations

2016
Let \(\mathbf{W} = (W^{1},\ldots,W^{m})\) be an m-dimensional Brownian motion, and let $$\displaystyle{\boldsymbol{\sigma }= (\sigma _{ij})_{1\leq i\leq d,1\leq j\leq m}: [0,\infty ) \times \mathbb{R}^{d} \rightarrow \mathbb{R}^{d} \times \mathbb{R}^{m}}$$ and $$\displaystyle{\boldsymbol{\mu }= (\mu ^{1},\ldots,\mu ^{d}): [0,\infty ) \times \
Paola Lecca, Angela Re, Adaoha Ihekwaba, Ivan Mura, Thanh-Phuong Nguyen   +4 more
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Stochastic partial differential equations

2014
Second order stochastic partial differential equations are discussed from a rough path point of view. In the linear and finite-dimensional noise case we follow a Feynman–Kac approach which makes good use of concentration of measure results, as those obtained in Sect. 11.2.
Peter K. Friz, Martin Hairer
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On a Class of Stochastic Differential Equations

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1963
AbstractStochastic differential equations of the type dy/dt + A(t) y = x(t) (A(t) being a matrix) are studied on the assumption that the random element is introduced only through x(t). Any component xi(t) of x(t) is characterised by the fact that in any finite interval (0,t) it undergoes only a finite number of discrete transitions, xi(t) remaining a ...
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Stochastic Differential Equations

2019
Abstract In this chapter we introduce stochastic differential equations (SDEs) and discuss existence and uniqueness questions. The geometric and linear equations are studied in some detail and their most important properties are derived. We then discuss the connection between SDEs and partial differential equations (PDEs).
V. Lakshmikantham, S.G. Deo
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Stochastic Differential Equations

2012
This chapter represents the core of the book. Building on the general theory introduced in previous chapters, stochastic differential equations (SDEs) are presented as a key mathematical tool for relating the subject of dynamical systems to Wiener noise.
Vincenzo Capasso, David Bakstein
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Stochastic Differential Equations

1990
A stochastic (ordinary) differential equation (SDE) usually looks like this $$d{X^i}(t) = {\mu _i}(t,X(t))dt + \sum\limits_{j = 1}^d {{\sigma _{ij}}(t,X(t))d{B^j}(t),\quad 1 \leqslant i \leqslant n.} $$ (11.0.1)
Heinrich von Weizsäcker, Gerhard Winkler   +1 more
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