Results 241 to 250 of about 105,333 (289)

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 Integrals and Differential Measures

Theory of Probability & Its Applications, 1988
The description of the class of measures with square integrable logarithmic derivative along a vector field and an operator field is obtained. This derivative coincides with an extended stochastic integral in the Gaussian case. The proofs are based on integration by parts.
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The Stochastic Integral

1990
In this chapter, we define (stochastic) Ito-integrals \(\int_0^t {HdM} \) H dM for local L 2 — martingales M and a fairly large class of adapted processes H. The integral is a random variable. It will be constructed as a suitable limit of Riemann-Stieltjes type approximations like $$\sum\limits_{i = 1}^n {{H_{{s_i}}} \cdot \left( {{M_{s{}_{i + 1}}}
Heinrich von Weizsäcker, Gerhard Winkler   +1 more
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The Stochastic Integral

2015
We have now established enough basic theory to construct the stochastic integral in full generality. In this chapter, we develop the integral with respect to semimartingales, and prove some of its properties. As in the previous chapters, we assume we have a filtered probability space, with filtration satisfying the usual conditions, \(\mathcal{F}_ ...
Samuel N. Cohen, Robert J. Elliott
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On a Generalization of a Stochastic Integral

Theory of Probability & Its Applications, 1976
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Path integrals and stochastic calculus

Advances in Physics, 2022
Vivien Lecomte, Frédéric van Wijland
exaly  

On an Identity for Stochastic Integrals

Theory of Probability & Its Applications, 1973
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The Stochastic Integral

2017
Let \(B = (\varOmega,\mathcal{F},(\mathcal{F}_{t})_{t},(B_{t})_{t},\mathrm{P})\) be a (continuous) standard Brownian motion fixed once and for all: the aim of this chapter is to give a meaning to expressions of the form \(\displaystyle{ \int _{0}^{T}X_{ s}(\omega )\,dB_{s}(\omega ) }\) where the integrand (X s )0 ≤ s ≤ T is a process enjoying certain ...
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Stochastic Integrals and Stochastic Functional Equations

SIAM Journal on Applied Mathematics, 1969
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Stochastic Integrals

Abstract This chapter has five sections and is concerned with the distribution of the ‘mean deviation’ components of the covariance described in Chapter 4. Section 1 shows how these terms can be rearranged in a useful manner, as the sums of products of an independent process and a moving average process whose weights are particular ...
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